Low Exercise Price Option - Revision history

en>Wikinista: LEPO Contract size is 100 not 1000, hasn't been since 2011

2014-07-21T18:35:59Z

LEPO Contract size is 100 not 1000, hasn't been since 2011

← Older revision		Revision as of 20:35, 21 July 2014
Line 1:		Line 1:
	~~{{about\|~~the ~~mathematical concept~~ of ~~Graph Algebras\|"Graph Algebra" as used in~~ the ~~social sciences\|Graph algebra (social sciences)}}~~		In workers break room I found out that the teachers here, despite their use of the internet in the classroom, do not know much about particular computers. They had one half hour long conversation if you must plug a working computer into a cell phone line so as to access the net. One teacher argued you was without to; the internet just existed in nothing. Another argued you needed a line. Of course the later was correct, but the shear amount of debate among the teachers, with neither side sounding certain themselves, informed me that teachers in this school were far less educated about computers versus teachers on my schools getting bigger.<br><br>Ideally, your book contract will specify an exact print run for your book. Many publishers will print 3000 books and are convinced this is the perfect print perform. Others will print 35,000 books. In rare instances, the number will uncover millions.<br><br>Don't embarrass your guests by preparing something likewise let just not meet their expectations. For one, wish to the right information along with that is generously given in this article for you to look over before beginning your effort.<br><br>If an individual might be just wearing the black tights and who are planning on-going out at night, some places may not let you in without a shirt (plus you may be a little cold in some places without one), as well as may to help buy a red, white, and blue wind jacket to wear with your tights or even USA Olympic T-shirt. But if a place will help you to go topless, go as it! As for shoes, just opt for simple black flip flops to survive look as you just threw them on after you bought out of your pool.<br><br>9) Tales and Tutus Performance Series - Sunday, October 31st 2PM / FREE - Headquarters Library Variety in the company's traditional dances for the goblins and monsters [[http://www.36barstools.com/2011/10/halloween-furniture-covers/ 36barstools.com]] season will be featured. Performance is right for all ages.<br><br>I did start to really notice how sexist certain students were today when a cupful of water was dropped on the surface. The male teacher cleaned up the water with sponges immediately. A ten year-old boy Turkish leaned over and said, "You haven't learned to do a job." The teacher snapped at him for saying such a rude thing, especially in advance of a female patient. Then he looked at me and gave us a very nervous smile and laugh.<br><br>CANDLE Cups. Decorate your own votive candle cups with patterns printed on backlight film, make certain put the film externally the mugs. Can be supplied as individual items, or in sets. Again personalised or how many candle selling outlets do you know? Make great Christmas christmas presents.<br><br>On the way back towards classroom I realized that the children in this particular school have much more freedom than I did in my schools as a child. For instance these were aloud walking back to classes ourselves. They are also aloud to go to the bathroom freely. But you are not void of supervision. Utilizing teachers' aides in the halls in addition, on the playgrounds. In addition there are older children called "Red Caps" who act as whistle blowers for plan.

	~~In [[mathematics]], especially~~ in the ~~fields of [[universal algebra]] and [[graph theory]]~~, a ~~'''graph algebra''' is~~ a ~~way of giving~~ a ~~[[directed graph]] an [[algebraic structure]]~~. It was ~~introduced in {{harv\|McNulty\|Shallon\|1983}}~~, ~~and has seen many uses in~~ the ~~field~~ of ~~universal algebra since then~~.

	~~== Definition ==~~

	~~Let~~ <~~math~~>~~D=(V,E)~~<~~/math~~> ~~be a directed [[graph (data structure)\|graph]]~~, and <~~math~~>0<~~/math~~> ~~an element~~ not ~~in <math>V</math>~~. ~~The graph algebra associated~~ with ~~<math>D</math>~~ is ~~the set~~ <~~math~~>~~V \cup \{0\}~~<~~/math~~> ~~equipped with multiplication defined by~~ the ~~rules~~
	* <math>xy = x</math> if <math>x,y\in V,(~~x,y~~)~~\in E</math>~~
	* <math>xy = 0</math> if <math>x,~~y\in V\cup \{0\}~~,(x,~~y)\notin E</math>~~.

	~~== Applications ==~~

	~~This notion has made~~ it ~~possible~~ to ~~use the methods~~ of ~~graph theory in universal algebra and several other directions of discrete mathematics and computer science~~. Graph algebras have been used, for example, in constructions concerning dualities {{harv\|Davey\|Idziak\|Lampe\|McNulty\|2000}}, [[equational theory\|equational theories]] {{harv\|Pöschel\|1989}}, [[flatness (systems theory)~~\|flatness]] {{harv\|Delić\|2001}}~~, ~~[[groupoid (algebra)\|groupoid]] [[ring (mathematics)\|ring]]s {{harv\|Lee\|1991}}, [[topology\|topologies]] {{harv\|Lee\|1988}}, [[variety (universal algebra)\|varieties]] {{harv\|Oates~~-~~Williams\|1984}}, [[finite state automata]] {{harv\|Kelarev\|Miller\|Sokratova\|2005}}, [[finite state machine]]~~s ~~{{harv\|Kelarev & Sokratova\|2003}},~~
	~~tree languages~~ and [[~~tree automata]] {{harv\|Kelarev\|Sokratova\|2001}} etc~~.

	~~== See also ==~~
	* [[Group algebra]]
	* [[Incidence algebra]]
	* [[Path algebra]]

	~~==References==~~
	*{{Citation \| last1=Davey \| first1=Brian A. ~~\| last2=Idziak \| first2=Pawel M. \| last3=Lampe \| first3=William A. \| last4=McNulty \| first4=George F. \| title=Dualizability and graph algebras \| doi=10.1016~~/~~S0012-365X(99)00225-3 \| id={{MathSciNet \| id = 1743633}} \| year=2000 \| journal=[[Discrete Mathematics (journal)\|Discrete Mathematics]] \| issn=0012-365X \| volume=214 \| issue=1 \| pages=145–172}}~~
	*{{Citation \| last1=Delić \| first1=Dejan \| title=Finite bases for flat graph algebras \| doi=10~~.1006~~/~~jabr.2001.8947 \| id={{MathSciNet \| id = 1872631}} \| year=2001 \| journal=Journal of Algebra \| issn=0021~~-~~8693 \| volume=246 \| issue=1 \| pages=453–469}}~~
	*{{Citation \| last1=McNulty \| first1=George F. \| last2=Shallon \| first2=Caroline R. \| title=Universal algebra and lattice theory (Puebla, 1982) \| publisher=[[Springer-~~Verlag]] \| location=Berlin, New York \| series=Lecture Notes in Math. \| doi=10.1007~~/~~BFb0063439 \| id={{MathSciNet \| id = 716184}} \| year=1983 \| volume=1004 \| chapter=Inherently nonfinitely based finite algebras \| pages=206–231}}~~
	*{{Citation \| last1=Kelarev \| first1=A.V. ~~\| title=''Graph Algebras and Automata'' \| publisher = [[Marcel Dekker~~]] \|
	~~year=2003 \| place=New York \| isbn=0-8247-4708-9 \| id={{MathSciNet \| id=2064147}} }}~~
	*{{Citation \| last1=Kelarev \| first1=A.V. ~~\| last2=Sokratova \| first2=O~~.V. \| year=2003 \| title=On congruences of automata defined by directed graphs \| journal=Theoretical Computer Science \| volume=301 \| issue=1–3 \| id={{MathSciNet \| id=1975219 }} \| pages=31–43 \| issn=0304-3975 \| doi=10.~~1016/S0304-3975(02)00544-3 }}~~
	*{{Citation \| last1=Kelarev \| first1=A~~.V. \| last2=Miller \| first2=M. \| last3=Sokratova \| first3=O.V. \|~~ year~~=2005 \| title=Languages recognized by two~~-~~sided automata of graphs \| journal=Proc. Estonian Akademy of Science \| volume=54 \| issue =1 \| pages=46–54 \| id={{MathSciNet \| id=2126358}} \| issn=1736-6046 }}~~
	*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Sokratova \| first2=O.V. \| year=2001 \| title=Directed graphs and ~~syntactic algebras of tree languages \| journal=J~~. ~~Automata~~, ~~Languages & Combinatorics \| volume=6 \| issue=3 \| pages=305–311 \| id={{MathSciNet \| id=1879773}} \| issn=1430-189X }}~~
	*{{Citation \| last1=Kiss \| first1=E.W. \| last2=Pöschel \| first2=R. \| last3=Pröhle \| first3=P. \| year=1990 \| title=Subvarieties of ~~varieties generated by graph algebras \| journal=Acta Sci~~. ~~Math~~. ~~(Szeged) \| volume=54 \| issue=1–2 \| pages=57–75 \| id={{MathSciNet \|id=1073419}} }}~~
	*{{Citation \| last1=Lee \| first1=S.-M. ~~\| year=1988 \| title=Graph algebras which admit only discrete topologies \| journal=Congr~~. ~~Numer~~. ~~\| volume=64 \| pages=147–156 \| id={{MathSciNet \|id=0988675}} \| issn=1736-6046 }}~~
	*{{Citation \| last1=Lee \| first=S.-M. ~~\| year=1991 \| title=Simple graph algebras and simple rings \| journal=Southeast Asian Bull~~. ~~Math~~. ~~\| volume=15 \| issue=2 \| pages=117–121 \| id={{MathSciNet \| id=1145431 }} \| issn=0129-2021 }}~~
	*{{Citation \| last1=Oates-Williams \| first1=Sheila \| title=On the ~~variety generated by Murskiĭ's algebra \| doi=10~~.~~1007/BF01198526 \| id={{MathSciNet \| id = 743465}} \| year=1984 \| journal=Algebra Universalis \| issn=0002-5240 \| volume=18 \| issue=2 \| pages=175–177}}~~
	*{{Citation \| doi=10.1002/malq.19890350311 \| last1=Pöschel \| first1=R \| year=1989 \| title=The equational logic for ~~graph algebras \| journal=Z. Math. Logik Grundlag~~. ~~Math. \| volume=35 \| issue=3 \| pages=273–282 \| id={{MathSciNet \| id=1000970}} }}~~

	~~==Further reading==~~
	*{{Citation \| title=Graph algebras \| author=Raeburn, Iain \| authorlink=Iain Raeburn \| year=2005 \| publisher=[[American Mathematical Society]] \| isbn=978-0-8218-3660-6}}

	~~[[Category:Universal algebra]]~~
	~~[[Category:Graph theory]]~~

en>Cydebot: Robot - Speedily moving category Options to :Category:Options (finance) per CFDS.

2013-11-09T08:04:33Z

Robot - Speedily moving category Options to Category:Options (finance) per CFDS.

← Older revision		Revision as of 10:04, 9 November 2013
Line 1:		Line 1:
	~~3 My name is Emmitt though Do not think really like being called like because. For years I~~'~~ve lived in Nh but now i~~'~~m considering other choices. Office supervising is how she supports her friends and she won~~'~~t change it anytime before long. The favorite hobby for the kids and me~~ is ~~playing croquet nevertheless i don't have~~ an ~~time over recent weeks~~. ~~Her husband~~ and ~~her maintain an online business website~~. ~~You may wish to check it out: http:~~//~~www~~.~~36barstools.com~~/~~2011~~/10/~~halloween-furniture-covers~~/<br><br>~~Also visit my web~~-~~site~~ ... ~~goblins~~ and ~~monsters~~ [[~~http:~~//~~www~~.~~36barstools~~.~~com~~/~~2011~~/10/~~halloween~~-~~furniture~~-~~covers/ 36barstools.com~~]]		{{about\|the mathematical concept of Graph Algebras\|"Graph Algebra" as used in the social sciences\|Graph algebra (social sciences)}}

			In [[mathematics]], especially in the fields of [[universal algebra]] and [[graph theory]], a '''graph algebra''' is a way of giving a [[directed graph]] an [[algebraic structure]]. It was introduced in {{harv\|McNulty\|Shallon\|1983}}, and has seen many uses in the field of universal algebra since then.

			== Definition ==

			Let <math>D=(V,E)</math> be a directed [[graph (data structure)\|graph]], and <math>0</math> an element not in <math>V</math>. The graph algebra associated with <math>D</math> is the set <math>V \cup \{0\}</math> equipped with multiplication defined by the rules
			* <math>xy = x</math> if <math>x,y\in V,(x,y)\in E</math>
			* <math>xy = 0</math> if <math>x,y\in V\cup \{0\},(x,y)\notin E</math>.

			== Applications ==

			This notion has made it possible to use the methods of graph theory in universal algebra and several other directions of discrete mathematics and computer science. Graph algebras have been used, for example, in constructions concerning dualities {{harv\|Davey\|Idziak\|Lampe\|McNulty\|2000}}, [[equational theory\|equational theories]] {{harv\|Pöschel\|1989}}, [[flatness (systems theory)\|flatness]] {{harv\|Delić\|2001}}, [[groupoid (algebra)\|groupoid]] [[ring (mathematics)\|ring]]s {{harv\|Lee\|1991}}, [[topology\|topologies]] {{harv\|Lee\|1988}}, [[variety (universal algebra)\|varieties]] {{harv\|Oates-Williams\|1984}}, [[finite state automata]] {{harv\|Kelarev\|Miller\|Sokratova\|2005}}, [[finite state machine]]s {{harv\|Kelarev & Sokratova\|2003}},
			tree languages and [[tree automata]] {{harv\|Kelarev\|Sokratova\|2001}} etc.

			== See also ==
			* [[Group algebra]]
			* [[Incidence algebra]]
			* [[Path algebra]]

			==References==
			*{{Citation \| last1=Davey \| first1=Brian A. \| last2=Idziak \| first2=Pawel M. \| last3=Lampe \| first3=William A. \| last4=McNulty \| first4=George F. \| title=Dualizability and graph algebras \| doi=10.1016/S0012-365X(99)00225-3 \| id={{MathSciNet \| id = 1743633}} \| year=2000 \| journal=[[Discrete Mathematics (journal)\|Discrete Mathematics]] \| issn=0012-365X \| volume=214 \| issue=1 \| pages=145–172}}
			*{{Citation \| last1=Delić \| first1=Dejan \| title=Finite bases for flat graph algebras \| doi=10.1006/jabr.2001.8947 \| id={{MathSciNet \| id = 1872631}} \| year=2001 \| journal=Journal of Algebra \| issn=0021-8693 \| volume=246 \| issue=1 \| pages=453–469}}
			*{{Citation \| last1=McNulty \| first1=George F. \| last2=Shallon \| first2=Caroline R. \| title=Universal algebra and lattice theory (Puebla, 1982) \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Lecture Notes in Math. \| doi=10.1007/BFb0063439 \| id={{MathSciNet \| id = 716184}} \| year=1983 \| volume=1004 \| chapter=Inherently nonfinitely based finite algebras \| pages=206–231}}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| title=''Graph Algebras and Automata'' \| publisher = [[Marcel Dekker]] \|
			year=2003 \| place=New York \| isbn=0-8247-4708-9 \| id={{MathSciNet \| id=2064147}} }}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Sokratova \| first2=O.V. \| year=2003 \| title=On congruences of automata defined by directed graphs \| journal=Theoretical Computer Science \| volume=301 \| issue=1–3 \| id={{MathSciNet \| id=1975219 }} \| pages=31–43 \| issn=0304-3975 \| doi=10.1016/S0304-3975(02)00544-3 }}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Miller \| first2=M. \| last3=Sokratova \| first3=O.V. \| year=2005 \| title=Languages recognized by two-sided automata of graphs \| journal=Proc. Estonian Akademy of Science \| volume=54 \| issue =1 \| pages=46–54 \| id={{MathSciNet \| id=2126358}} \| issn=1736-6046 }}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Sokratova \| first2=O.V. \| year=2001 \| title=Directed graphs and syntactic algebras of tree languages \| journal=J. Automata, Languages & Combinatorics \| volume=6 \| issue=3 \| pages=305–311 \| id={{MathSciNet \| id=1879773}} \| issn=1430-189X }}
			*{{Citation \| last1=Kiss \| first1=E.W. \| last2=Pöschel \| first2=R. \| last3=Pröhle \| first3=P. \| year=1990 \| title=Subvarieties of varieties generated by graph algebras \| journal=Acta Sci. Math. (Szeged) \| volume=54 \| issue=1–2 \| pages=57–75 \| id={{MathSciNet \|id=1073419}} }}
			*{{Citation \| last1=Lee \| first1=S.-M. \| year=1988 \| title=Graph algebras which admit only discrete topologies \| journal=Congr. Numer. \| volume=64 \| pages=147–156 \| id={{MathSciNet \|id=0988675}} \| issn=1736-6046 }}
			*{{Citation \| last1=Lee \| first=S.-M. \| year=1991 \| title=Simple graph algebras and simple rings \| journal=Southeast Asian Bull. Math. \| volume=15 \| issue=2 \| pages=117–121 \| id={{MathSciNet \| id=1145431 }} \| issn=0129-2021 }}
			*{{Citation \| last1=Oates-Williams \| first1=Sheila \| title=On the variety generated by Murskiĭ's algebra \| doi=10.1007/BF01198526 \| id={{MathSciNet \| id = 743465}} \| year=1984 \| journal=Algebra Universalis \| issn=0002-5240 \| volume=18 \| issue=2 \| pages=175–177}}
			*{{Citation \| doi=10.1002/malq.19890350311 \| last1=Pöschel \| first1=R \| year=1989 \| title=The equational logic for graph algebras \| journal=Z. Math. Logik Grundlag. Math. \| volume=35 \| issue=3 \| pages=273–282 \| id={{MathSciNet \| id=1000970}} }}

			==Further reading==
			*{{Citation \| title=Graph algebras \| author=Raeburn, Iain \| authorlink=Iain Raeburn \| year=2005 \| publisher=[[American Mathematical Society]] \| isbn=978-0-8218-3660-6}}

			[[Category:Universal algebra]]
			[[Category:Graph theory]]

en>CaptinJohn: Changed "European" link to point to the Option Type instead of the Continent. ~~~~

2012-08-23T13:47:39Z

Changed "European" link to point to the Option Type instead of the Continent. ~~~~

New page

3 My name is Emmitt though Do not think really like being called like because. For years I've lived in Nh but now i'm considering other choices. Office supervising is how she supports her friends and she won't change it anytime before long. The favorite hobby for the kids and me is playing croquet nevertheless i don't have an time over recent weeks. Her husband and her maintain an online business website. You may wish to check it out: http://www.36barstools.com/2011/10/halloween-furniture-covers/<br><br>Also visit my web-site ... goblins and monsters [[http://www.36barstools.com/2011/10/halloween-furniture-covers/ 36barstools.com]]

← Older revision		Revision as of 20:35, 21 July 2014
Line 1:		Line 1:
	~~{{about\|~~the ~~mathematical concept~~ of ~~Graph Algebras\|"Graph Algebra" as used in~~ the ~~social sciences\|Graph algebra (social sciences)}}~~		In workers break room I found out that the teachers here, despite their use of the internet in the classroom, do not know much about particular computers. They had one half hour long conversation if you must plug a working computer into a cell phone line so as to access the net. One teacher argued you was without to; the internet just existed in nothing. Another argued you needed a line. Of course the later was correct, but the shear amount of debate among the teachers, with neither side sounding certain themselves, informed me that teachers in this school were far less educated about computers versus teachers on my schools getting bigger.<br><br>Ideally, your book contract will specify an exact print run for your book. Many publishers will print 3000 books and are convinced this is the perfect print perform. Others will print 35,000 books. In rare instances, the number will uncover millions.<br><br>Don't embarrass your guests by preparing something likewise let just not meet their expectations. For one, wish to the right information along with that is generously given in this article for you to look over before beginning your effort.<br><br>If an individual might be just wearing the black tights and who are planning on-going out at night, some places may not let you in without a shirt (plus you may be a little cold in some places without one), as well as may to help buy a red, white, and blue wind jacket to wear with your tights or even USA Olympic T-shirt. But if a place will help you to go topless, go as it! As for shoes, just opt for simple black flip flops to survive look as you just threw them on after you bought out of your pool.<br><br>9) Tales and Tutus Performance Series - Sunday, October 31st 2PM / FREE - Headquarters Library Variety in the company's traditional dances for the goblins and monsters [[http://www.36barstools.com/2011/10/halloween-furniture-covers/ 36barstools.com]] season will be featured. Performance is right for all ages.<br><br>I did start to really notice how sexist certain students were today when a cupful of water was dropped on the surface. The male teacher cleaned up the water with sponges immediately. A ten year-old boy Turkish leaned over and said, "You haven't learned to do a job." The teacher snapped at him for saying such a rude thing, especially in advance of a female patient. Then he looked at me and gave us a very nervous smile and laugh.<br><br>CANDLE Cups. Decorate your own votive candle cups with patterns printed on backlight film, make certain put the film externally the mugs. Can be supplied as individual items, or in sets. Again personalised or how many candle selling outlets do you know? Make great Christmas christmas presents.<br><br>On the way back towards classroom I realized that the children in this particular school have much more freedom than I did in my schools as a child. For instance these were aloud walking back to classes ourselves. They are also aloud to go to the bathroom freely. But you are not void of supervision. Utilizing teachers' aides in the halls in addition, on the playgrounds. In addition there are older children called "Red Caps" who act as whistle blowers for plan.

	~~In [[mathematics]], especially~~ in the ~~fields of [[universal algebra]] and [[graph theory]]~~, a ~~'''graph algebra''' is~~ a ~~way of giving~~ a ~~[[directed graph]] an [[algebraic structure]]~~. It was ~~introduced in {{harv\|McNulty\|Shallon\|1983}}~~, ~~and has seen many uses in~~ the ~~field~~ of ~~universal algebra since then~~.

	~~== Definition ==~~

	~~Let~~ <~~math~~>~~D=(V,E)~~<~~/math~~> ~~be a directed [[graph (data structure)\|graph]]~~, and <~~math~~>0<~~/math~~> ~~an element~~ not ~~in <math>V</math>~~. ~~The graph algebra associated~~ with ~~<math>D</math>~~ is ~~the set~~ <~~math~~>~~V \cup \{0\}~~<~~/math~~> ~~equipped with multiplication defined by~~ the ~~rules~~
	* <math>xy = x</math> if <math>x,y\in V,(~~x,y~~)~~\in E</math>~~
	* <math>xy = 0</math> if <math>x,~~y\in V\cup \{0\}~~,(x,~~y)\notin E</math>~~.

	~~== Applications ==~~

	~~This notion has made~~ it ~~possible~~ to ~~use the methods~~ of ~~graph theory in universal algebra and several other directions of discrete mathematics and computer science~~. Graph algebras have been used, for example, in constructions concerning dualities {{harv\|Davey\|Idziak\|Lampe\|McNulty\|2000}}, [[equational theory\|equational theories]] {{harv\|Pöschel\|1989}}, [[flatness (systems theory)~~\|flatness]] {{harv\|Delić\|2001}}~~, ~~[[groupoid (algebra)\|groupoid]] [[ring (mathematics)\|ring]]s {{harv\|Lee\|1991}}, [[topology\|topologies]] {{harv\|Lee\|1988}}, [[variety (universal algebra)\|varieties]] {{harv\|Oates~~-~~Williams\|1984}}, [[finite state automata]] {{harv\|Kelarev\|Miller\|Sokratova\|2005}}, [[finite state machine]]~~s ~~{{harv\|Kelarev & Sokratova\|2003}},~~
	~~tree languages~~ and [[~~tree automata]] {{harv\|Kelarev\|Sokratova\|2001}} etc~~.

	~~== See also ==~~
	* [[Group algebra]]
	* [[Incidence algebra]]
	* [[Path algebra]]

	~~==References==~~
	*{{Citation \| last1=Davey \| first1=Brian A. ~~\| last2=Idziak \| first2=Pawel M. \| last3=Lampe \| first3=William A. \| last4=McNulty \| first4=George F. \| title=Dualizability and graph algebras \| doi=10.1016~~/~~S0012-365X(99)00225-3 \| id={{MathSciNet \| id = 1743633}} \| year=2000 \| journal=[[Discrete Mathematics (journal)\|Discrete Mathematics]] \| issn=0012-365X \| volume=214 \| issue=1 \| pages=145–172}}~~
	*{{Citation \| last1=Delić \| first1=Dejan \| title=Finite bases for flat graph algebras \| doi=10~~.1006~~/~~jabr.2001.8947 \| id={{MathSciNet \| id = 1872631}} \| year=2001 \| journal=Journal of Algebra \| issn=0021~~-~~8693 \| volume=246 \| issue=1 \| pages=453–469}}~~
	*{{Citation \| last1=McNulty \| first1=George F. \| last2=Shallon \| first2=Caroline R. \| title=Universal algebra and lattice theory (Puebla, 1982) \| publisher=[[Springer-~~Verlag]] \| location=Berlin, New York \| series=Lecture Notes in Math. \| doi=10.1007~~/~~BFb0063439 \| id={{MathSciNet \| id = 716184}} \| year=1983 \| volume=1004 \| chapter=Inherently nonfinitely based finite algebras \| pages=206–231}}~~
	*{{Citation \| last1=Kelarev \| first1=A.V. ~~\| title=''Graph Algebras and Automata'' \| publisher = [[Marcel Dekker~~]] \|
	~~year=2003 \| place=New York \| isbn=0-8247-4708-9 \| id={{MathSciNet \| id=2064147}} }}~~
	*{{Citation \| last1=Kelarev \| first1=A.V. ~~\| last2=Sokratova \| first2=O~~.V. \| year=2003 \| title=On congruences of automata defined by directed graphs \| journal=Theoretical Computer Science \| volume=301 \| issue=1–3 \| id={{MathSciNet \| id=1975219 }} \| pages=31–43 \| issn=0304-3975 \| doi=10.~~1016/S0304-3975(02)00544-3 }}~~
	*{{Citation \| last1=Kelarev \| first1=A~~.V. \| last2=Miller \| first2=M. \| last3=Sokratova \| first3=O.V. \|~~ year~~=2005 \| title=Languages recognized by two~~-~~sided automata of graphs \| journal=Proc. Estonian Akademy of Science \| volume=54 \| issue =1 \| pages=46–54 \| id={{MathSciNet \| id=2126358}} \| issn=1736-6046 }}~~
	*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Sokratova \| first2=O.V. \| year=2001 \| title=Directed graphs and ~~syntactic algebras of tree languages \| journal=J~~. ~~Automata~~, ~~Languages & Combinatorics \| volume=6 \| issue=3 \| pages=305–311 \| id={{MathSciNet \| id=1879773}} \| issn=1430-189X }}~~
	*{{Citation \| last1=Kiss \| first1=E.W. \| last2=Pöschel \| first2=R. \| last3=Pröhle \| first3=P. \| year=1990 \| title=Subvarieties of ~~varieties generated by graph algebras \| journal=Acta Sci~~. ~~Math~~. ~~(Szeged) \| volume=54 \| issue=1–2 \| pages=57–75 \| id={{MathSciNet \|id=1073419}} }}~~
	*{{Citation \| last1=Lee \| first1=S.-M. ~~\| year=1988 \| title=Graph algebras which admit only discrete topologies \| journal=Congr~~. ~~Numer~~. ~~\| volume=64 \| pages=147–156 \| id={{MathSciNet \|id=0988675}} \| issn=1736-6046 }}~~
	*{{Citation \| last1=Lee \| first=S.-M. ~~\| year=1991 \| title=Simple graph algebras and simple rings \| journal=Southeast Asian Bull~~. ~~Math~~. ~~\| volume=15 \| issue=2 \| pages=117–121 \| id={{MathSciNet \| id=1145431 }} \| issn=0129-2021 }}~~
	*{{Citation \| last1=Oates-Williams \| first1=Sheila \| title=On the ~~variety generated by Murskiĭ's algebra \| doi=10~~.~~1007/BF01198526 \| id={{MathSciNet \| id = 743465}} \| year=1984 \| journal=Algebra Universalis \| issn=0002-5240 \| volume=18 \| issue=2 \| pages=175–177}}~~
	*{{Citation \| doi=10.1002/malq.19890350311 \| last1=Pöschel \| first1=R \| year=1989 \| title=The equational logic for ~~graph algebras \| journal=Z. Math. Logik Grundlag~~. ~~Math. \| volume=35 \| issue=3 \| pages=273–282 \| id={{MathSciNet \| id=1000970}} }}~~

	~~==Further reading==~~
	*{{Citation \| title=Graph algebras \| author=Raeburn, Iain \| authorlink=Iain Raeburn \| year=2005 \| publisher=[[American Mathematical Society]] \| isbn=978-0-8218-3660-6}}

	~~[[Category:Universal algebra]]~~
	~~[[Category:Graph theory]]~~

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	~~3 My name is Emmitt though Do not think really like being called like because. For years I~~'~~ve lived in Nh but now i~~'~~m considering other choices. Office supervising is how she supports her friends and she won~~'~~t change it anytime before long. The favorite hobby for the kids and me~~ is ~~playing croquet nevertheless i don't have~~ an ~~time over recent weeks~~. ~~Her husband~~ and ~~her maintain an online business website~~. ~~You may wish to check it out: http:~~//~~www~~.~~36barstools.com~~/~~2011~~/10/~~halloween-furniture-covers~~/<br><br>~~Also visit my web~~-~~site~~ ... ~~goblins~~ and ~~monsters~~ [[~~http:~~//~~www~~.~~36barstools~~.~~com~~/~~2011~~/10/~~halloween~~-~~furniture~~-~~covers/ 36barstools.com~~]]		{{about\|the mathematical concept of Graph Algebras\|"Graph Algebra" as used in the social sciences\|Graph algebra (social sciences)}}

			In [[mathematics]], especially in the fields of [[universal algebra]] and [[graph theory]], a '''graph algebra''' is a way of giving a [[directed graph]] an [[algebraic structure]]. It was introduced in {{harv\|McNulty\|Shallon\|1983}}, and has seen many uses in the field of universal algebra since then.

			== Definition ==

			Let <math>D=(V,E)</math> be a directed [[graph (data structure)\|graph]], and <math>0</math> an element not in <math>V</math>. The graph algebra associated with <math>D</math> is the set <math>V \cup \{0\}</math> equipped with multiplication defined by the rules
			* <math>xy = x</math> if <math>x,y\in V,(x,y)\in E</math>
			* <math>xy = 0</math> if <math>x,y\in V\cup \{0\},(x,y)\notin E</math>.

			== Applications ==

			This notion has made it possible to use the methods of graph theory in universal algebra and several other directions of discrete mathematics and computer science. Graph algebras have been used, for example, in constructions concerning dualities {{harv\|Davey\|Idziak\|Lampe\|McNulty\|2000}}, [[equational theory\|equational theories]] {{harv\|Pöschel\|1989}}, [[flatness (systems theory)\|flatness]] {{harv\|Delić\|2001}}, [[groupoid (algebra)\|groupoid]] [[ring (mathematics)\|ring]]s {{harv\|Lee\|1991}}, [[topology\|topologies]] {{harv\|Lee\|1988}}, [[variety (universal algebra)\|varieties]] {{harv\|Oates-Williams\|1984}}, [[finite state automata]] {{harv\|Kelarev\|Miller\|Sokratova\|2005}}, [[finite state machine]]s {{harv\|Kelarev & Sokratova\|2003}},
			tree languages and [[tree automata]] {{harv\|Kelarev\|Sokratova\|2001}} etc.

			== See also ==
			* [[Group algebra]]
			* [[Incidence algebra]]
			* [[Path algebra]]

			==References==
			*{{Citation \| last1=Davey \| first1=Brian A. \| last2=Idziak \| first2=Pawel M. \| last3=Lampe \| first3=William A. \| last4=McNulty \| first4=George F. \| title=Dualizability and graph algebras \| doi=10.1016/S0012-365X(99)00225-3 \| id={{MathSciNet \| id = 1743633}} \| year=2000 \| journal=[[Discrete Mathematics (journal)\|Discrete Mathematics]] \| issn=0012-365X \| volume=214 \| issue=1 \| pages=145–172}}
			*{{Citation \| last1=Delić \| first1=Dejan \| title=Finite bases for flat graph algebras \| doi=10.1006/jabr.2001.8947 \| id={{MathSciNet \| id = 1872631}} \| year=2001 \| journal=Journal of Algebra \| issn=0021-8693 \| volume=246 \| issue=1 \| pages=453–469}}
			*{{Citation \| last1=McNulty \| first1=George F. \| last2=Shallon \| first2=Caroline R. \| title=Universal algebra and lattice theory (Puebla, 1982) \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Lecture Notes in Math. \| doi=10.1007/BFb0063439 \| id={{MathSciNet \| id = 716184}} \| year=1983 \| volume=1004 \| chapter=Inherently nonfinitely based finite algebras \| pages=206–231}}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| title=''Graph Algebras and Automata'' \| publisher = [[Marcel Dekker]] \|
			year=2003 \| place=New York \| isbn=0-8247-4708-9 \| id={{MathSciNet \| id=2064147}} }}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Sokratova \| first2=O.V. \| year=2003 \| title=On congruences of automata defined by directed graphs \| journal=Theoretical Computer Science \| volume=301 \| issue=1–3 \| id={{MathSciNet \| id=1975219 }} \| pages=31–43 \| issn=0304-3975 \| doi=10.1016/S0304-3975(02)00544-3 }}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Miller \| first2=M. \| last3=Sokratova \| first3=O.V. \| year=2005 \| title=Languages recognized by two-sided automata of graphs \| journal=Proc. Estonian Akademy of Science \| volume=54 \| issue =1 \| pages=46–54 \| id={{MathSciNet \| id=2126358}} \| issn=1736-6046 }}
			*{{Citation \| last1=Kelarev \| first1=A.V. \| last2=Sokratova \| first2=O.V. \| year=2001 \| title=Directed graphs and syntactic algebras of tree languages \| journal=J. Automata, Languages & Combinatorics \| volume=6 \| issue=3 \| pages=305–311 \| id={{MathSciNet \| id=1879773}} \| issn=1430-189X }}
			*{{Citation \| last1=Kiss \| first1=E.W. \| last2=Pöschel \| first2=R. \| last3=Pröhle \| first3=P. \| year=1990 \| title=Subvarieties of varieties generated by graph algebras \| journal=Acta Sci. Math. (Szeged) \| volume=54 \| issue=1–2 \| pages=57–75 \| id={{MathSciNet \|id=1073419}} }}
			*{{Citation \| last1=Lee \| first1=S.-M. \| year=1988 \| title=Graph algebras which admit only discrete topologies \| journal=Congr. Numer. \| volume=64 \| pages=147–156 \| id={{MathSciNet \|id=0988675}} \| issn=1736-6046 }}
			*{{Citation \| last1=Lee \| first=S.-M. \| year=1991 \| title=Simple graph algebras and simple rings \| journal=Southeast Asian Bull. Math. \| volume=15 \| issue=2 \| pages=117–121 \| id={{MathSciNet \| id=1145431 }} \| issn=0129-2021 }}
			*{{Citation \| last1=Oates-Williams \| first1=Sheila \| title=On the variety generated by Murskiĭ's algebra \| doi=10.1007/BF01198526 \| id={{MathSciNet \| id = 743465}} \| year=1984 \| journal=Algebra Universalis \| issn=0002-5240 \| volume=18 \| issue=2 \| pages=175–177}}
			*{{Citation \| doi=10.1002/malq.19890350311 \| last1=Pöschel \| first1=R \| year=1989 \| title=The equational logic for graph algebras \| journal=Z. Math. Logik Grundlag. Math. \| volume=35 \| issue=3 \| pages=273–282 \| id={{MathSciNet \| id=1000970}} }}

			==Further reading==
			*{{Citation \| title=Graph algebras \| author=Raeburn, Iain \| authorlink=Iain Raeburn \| year=2005 \| publisher=[[American Mathematical Society]] \| isbn=978-0-8218-3660-6}}

			[[Category:Universal algebra]]
			[[Category:Graph theory]]