en>GoingBatty: Converted {{Multiple issues}} to new format to fix expert parameter using AWB (10617)

2015-01-09T04:03:48Z

Converted {{Multiple issues}} to new format to fix expert parameter using AWB (10617)

← Older revision		Revision as of 06:03, 9 January 2015
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	In [~~[mathematics]~~]~~, a '''monogenic field''' is an [[algebraic number field]] ''K''~~ for ~~which there exists an element ''a'' such that the [[ring of integers]] ''O''~~<~~sub~~>~~''K''~~<~~/sub~~> is the [~~[polynomial ring]] '''Z'''[''a''~~]. ~~The powers~~ of ~~such an element '~~'a~~'' constitute~~ a '~~''power integral basis'''~~.		be chic [http://www.thirumalaicharitytrust.org/brand/mk.asp?Topic=105 www.thirumalaicharitytrust.org/brand/mk.asp?Topic=105] for less this fall<br><br>They key is to have fuss free hair that let's the [https://www.flickr.com/search/?q=accessories accessories] do the talking for you and not overly done up.. Sure, have top of the line training facilities and they've been hoovering up young talent everywhere they find it, but if Kenny Dalglish is something of a poet at heart, Roberto Mancini is a construction foreman. <br><br>[http://opthalworld.com/brand/nike.asp?Topic=14 nike free run 3.0 tiffany blue] This represents the smallest market but the highest price point. "I was left alone in the house or in the car, and I'd listen to Van Morrison, and songs like I Miss You by Randy Newman, or anything by Harry Nilsson or Simple Man by Graham Nash. Last year, Coach made a run at Tory Burch, which along with Kate Spade is a prominent private company in the high but not too high end retailing niche. <br><br>[Telegraph] all the frenzy of Paris Fashion Week, singer Lily Allen was spotted patiently waiting for Karl Lagerfeld at Chanel to fit her wedding dress. The family posed for a much hyped 22 page spread in the October issue of the glossy publication, which was shot by [ [Read More]. <br><br>If you feel you have bushy eyebrows, and you want them gone, either pluck,thread or wax. Laura will be more pregnant, which leaves me to ponder just how she manages to be a mother of five, pregnant with the sixth (hopefully, a girl or a future drag queen, because of the overexposure to fashion while in Utero), and design her first fashion collection for runway presentation. <br><br>His textbook, "Basics of Induction Heating," was published in 1960. I had this invoice that was due to pay for them wholesale, so I started giving books away. Chairman and CEO John Idol commented on the results, "We are pleased with the strong start to our fiscal year with a 71% increase in total revenue and 185% growth in [http://www.thirumalaicharitytrust.org/brand/mk.asp?Topic=31 www.thirumalaicharitytrust.org/brand/mk.asp?Topic=31] net income. <br><br>It gives you time to hit the gym hard so the illusion can be a reality by summertime. Spanning more than 8.2 million square feet throughout major United States markets and Puerto Rico, Prime Retail is home to more than 400 leading designer and name brands such as Gucci, Giorgio Armani, Burberry, kate spade, Michael Kors, St. <br><br>So resellers should always [http://madrashardtools.com/brand/mk.asp?Topic=3 cheap michael kors purses] pay cash and never give their name!Carolyn 4 years agoI just received [http://www.spurindia.com/brand/coach.asp www.spurindia.com/brand/coach.asp] one of the letters from Coach saying I am no longer allowed to purchase from them because of the large [http://wordpress.org/search/quantity quantity] of bags I am purchasing. Although, since [https://www.google.com/search?hl=en&gl=us&tbm=nws&q=David+Beckham&btnI=lucky David Beckham] has been spotted wearing Superdry, it hasn't been so underground or indie. <br><br>Most designers offer collections every season which provide both high end and lower priced products. But CSN's problem is that they always interview the same people over and over. 36 this year with wealth of $1.06 billion, has an eye out for hotels, for instance, daughter Wendy recently told Forbes Asia..

	In a ~~monogenic field ''K''~~, the [~~[Discriminant of an algebraic number field\|field discriminant]~~] of ~~''K'' is equal~~ to the ~~[[discriminant]]~~ of the [[~~Minimal polynomial (field theory)\|minimal polynomial~~]~~] of α~~.

	~~==Examples==~~
	~~Examples of monogenic fields include:~~
	* [[Quadratic fields]]:
	~~: if~~ <~~math~~>~~K = \mathbf{Q}(\sqrt d)~~<~~/math~~> with <~~math~~>d<~~/math~~> a [~~[square-free integer]], then <math>O_K~~ = ~~\mathbf{Z}[a~~]<~~/math~~> ~~where~~ <~~math~~>a ~~= (1+\sqrt d)/~~2<~~/math~~> ~~if ''d''≡1 (mod 4) and~~ <~~math~~>a = ~~\sqrt d</math> if ''d'' ≡ 2 or~~ 3 ~~(mod~~ 4).
	* [[~~Cyclotomic fields]]~~:
	~~: if <math>K = \mathbf{Q}(\zeta)<~~/~~math> with <math>\zeta<~~/~~math> a [[root of unity]], then <math>O_K = \mathbf{Z}[\zeta]~~.</~~math>~~

	~~Not all number fields are monogenic; [[Richard Dedekind~~]~~] gave~~ the ~~example~~ of the [~~[cubic field~~]~~] generated by a root~~ of ~~the polynomial <math>X^3 - X^2 - 2X - 8~~.</~~math>~~

	==~~References~~==
	* {{cite book \| last = ~~Narkiewicz \| first = Władysław \| authorlink = \| title = Elementary~~ and ~~Analytic Theory~~ of ~~Algebraic Numbers \| publisher = [[Springer-Verlag]] \| date = 2004 \| location = \| page = 64 \| isbn = 3-540-21902-~~1 ~~\| edition=3rd \| zbl=1159~~.~~11039}}~~
	* {{cite book \| last = Gaál \| first = István \| authorlink = \| title = Diophantine Equations and Power Integral Bases \| publisher = [[Birkhäuser Verlag]] \| date = 2002 \| location = Boston, ~~MA \| isbn = 978-0-8176-4271-6 \| zbl=1016~~.~~11059 }}~~

	~~[[Category:Algebraic number theory]]~~

	~~{{Numtheory-stub}}~~

en>Wesarah30: about Sarah

2013-12-16T23:08:20Z

about Sarah

← Older revision		Revision as of 01:08, 17 December 2013
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	~~Hello~~, I'~~m Darell,~~ a ~~24 year old from Cleveland Heights~~, ~~United States~~.<br>~~My hobbies include~~ (~~but are not limited to~~) ~~Rugby league football~~, ~~Badminton~~ and ~~watching Breaking Bad.~~<br><br>~~Here is my web blog~~ :: ~~[http:~~//~~www~~.~~thirumalaicharitytrust~~.~~org~~/~~brand/mk~~.~~asp?Topic~~=~~105 www~~.~~thirumalaicharitytrust.org/brand/mk.asp?Topic=105~~]		In [[mathematics]], a '''monogenic field''' is an [[algebraic number field]] ''K'' for which there exists an element ''a'' such that the [[ring of integers]] ''O''<sub>''K''</sub> is the [[polynomial ring]] '''Z'''[''a'']. The powers of such an element ''a'' constitute a '''power integral basis'''.

			In a monogenic field ''K'', the [[Discriminant of an algebraic number field\|field discriminant]] of ''K'' is equal to the [[discriminant]] of the [[Minimal polynomial (field theory)\|minimal polynomial]] of α.

			==Examples==
			Examples of monogenic fields include:
			* [[Quadratic fields]]:
			: if <math>K = \mathbf{Q}(\sqrt d)</math> with <math>d</math> a [[square-free integer]], then <math>O_K = \mathbf{Z}[a]</math> where <math>a = (1+\sqrt d)/2</math> if ''d''≡1 (mod 4) and <math>a = \sqrt d</math> if ''d'' ≡ 2 or 3 (mod 4).
			* [[Cyclotomic fields]]:
			: if <math>K = \mathbf{Q}(\zeta)</math> with <math>\zeta</math> a [[root of unity]], then <math>O_K = \mathbf{Z}[\zeta].</math>

			Not all number fields are monogenic; [[Richard Dedekind]] gave the example of the [[cubic field]] generated by a root of the polynomial <math>X^3 - X^2 - 2X - 8.</math>

			==References==
			* {{cite book \| last = Narkiewicz \| first = Władysław \| authorlink = \| title = Elementary and Analytic Theory of Algebraic Numbers \| publisher = [[Springer-Verlag]] \| date = 2004 \| location = \| page = 64 \| isbn = 3-540-21902-1 \| edition=3rd \| zbl=1159.11039}}
			* {{cite book \| last = Gaál \| first = István \| authorlink = \| title = Diophantine Equations and Power Integral Bases \| publisher = [[Birkhäuser Verlag]] \| date = 2002 \| location = Boston, MA \| isbn = 978-0-8176-4271-6 \| zbl=1016.11059 }}

			[[Category:Algebraic number theory]]

			{{Numtheory-stub}}

en>Woohookitty: WikiCleaner 0.99 - Repairing link to disambiguation page - (You can help) - Operator

2011-01-03T06:14:39Z

WikiCleaner 0.99 - Repairing link to disambiguation page - (You can help) - Operator

New page

Hello, I'm Darell, a 24 year old from Cleveland Heights, United States.<br>My hobbies include (but are not limited to) Rugby league football, Badminton and watching Breaking Bad.<br><br>Here is my web blog :: [http://www.thirumalaicharitytrust.org/brand/mk.asp?Topic=105 www.thirumalaicharitytrust.org/brand/mk.asp?Topic=105]

Symmetric convolution - Revision history

en>GoingBatty: Converted {{Multiple issues}} to new format to fix expert parameter using AWB (10617)

en>Wesarah30: about Sarah

en>Woohookitty: WikiCleaner 0.99 - Repairing link to disambiguation page - (You can help) - Operator