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| {{Unreferenced|date=December 2009}}
| | Greetings. The author's name is Isobel but she never really liked that name. He's always loved living in New Mexico. As a girl what I like is playing dominoes but i don't offer the time currently. Invoicing already been my employment for a little while but I've always wanted my own business. I'm no real at webdesign but stores want to be sure of my website: http://www.43things.com/entries/view/6515440<br><br>Feel free to surf to my web blog :: epoxi resina - [http://www.43things.com/entries/view/6515440 made a post], |
| The term '''center''' or '''centre''' is used in various contexts in [[abstract algebra]] to denote the set of all those elements that [[commutative operation|commute]] with all other elements. It is often denoted ''Z,'' from German ''[[wikt:Zentrum|Zentrum]],'' meaning "center". More specifically: | |
| * The '''[[center of a group]]''' ''G'' consists of all those elements ''x'' in ''G'' such that ''xg'' = ''gx'' for all ''g'' in ''G''. This is a [[normal subgroup]] of ''G''.
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| * The center of a [[ring (mathematics)|ring]] ''R'' is the subset of ''R'' consisting of all those elements ''x'' of ''R'' such that ''xr'' = ''rx'' for all ''r'' in ''R''. The center is a [[commutative ring|commutative]] [[subring]] of ''R'', and ''R'' is an [[algebra (ring theory)|algebra]] over its center.
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| * The center of an [[algebra over a field|algebra]] ''A'' consists of all those elements ''x'' of ''A'' such that ''xa'' = ''ax'' for all ''a'' in ''A''. See also: [[central simple algebra]].
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| * The center of a [[Lie algebra]] ''L'' consists of all those elements ''x'' in ''L'' such that [''x'',''a''] = 0 for all ''a'' in ''L''. This is an [[ideal (ring theory)|ideal]] of the Lie algebra ''L''.
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| * The [[centre (category)|center]] of a [[monoidal category]] '''C''' consists of pairs ''(A,u)'' where ''A'' is an object of '''C''', and <math>u:A \otimes - \rightarrow - \otimes A</math> a natural isomorphism satisfying certain axioms.
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| == See also ==
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| *[[Centralizer and normalizer]]
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| == References ==
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| Modern Algebra, R. Durbin, 3rd edition (1992), page 118, exercise 22.22
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| {{DEFAULTSORT:Center (Algebra)}}
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| [[Category:Abstract algebra]]
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Latest revision as of 19:17, 2 March 2014
Greetings. The author's name is Isobel but she never really liked that name. He's always loved living in New Mexico. As a girl what I like is playing dominoes but i don't offer the time currently. Invoicing already been my employment for a little while but I've always wanted my own business. I'm no real at webdesign but stores want to be sure of my website: http://www.43things.com/entries/view/6515440
Feel free to surf to my web blog :: epoxi resina - made a post,