Rational mapping - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T21:11:14Z

References: replace mr template with mr parameter in CS1 templates; using AWB

← Older revision		Revision as of 23:11, 25 September 2014
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	~~In [[algebraic geometry]]~~, ~~a '''noetherian scheme''' is a [[scheme (mathematics)\|scheme]] that admits a finite covering by open affine subsets <math>\operatorname{Spec} A_i</math>, <math>A_i</math> [[noetherian rings]]~~. ~~More generally, a scheme~~ is ~~'''locally noetherian''' if it is covered by spectra~~ of ~~noetherian rings~~. ~~Thus, a scheme~~ is ~~noetherian if~~ and ~~only if~~ it ~~is locally noetherian and quasi-compact.~~ ~~As with noetherian rings, the concept is named after~~ [~~[Emmy Noether]]~~.		Hi there, I am Andrew Berryhill. To play lacross is the thing I adore most of all. Distributing production is exactly where my main earnings arrives from and it's something I truly free tarot readings; [http://kpupf.com/xe/talk/735373 kpupf.com], appreciate. I've always cherished residing in Kentucky but now I'm considering other options.<br><br>Feel free to visit my weblog ... free psychic readings - [http://cartoonkorea.com/ce002/1093612 click this link here now] - online reader - [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies Click On this page],

	~~It can be shown that, in a locally noetherian scheme, if  <math>\operatorname{Spec} A<~~/~~math> is an open affine subset, then ''A'' is a noetherian ring~~. ~~In particular~~, ~~<math>\operatorname{Spec} A</math> is a noetherian scheme if and only if ''A'' is a noetherian ring~~. ~~Let~~ ''~~X'' be a locally noetherian scheme~~. ~~Then the local rings~~ <~~math~~>~~\mathcal{O}_{X, x}~~<~~/math~~> ~~are noetherian rings~~.

	~~A noetherian scheme is a [[noetherian topological space]]~~. ~~But the converse is false in general; consider, for example, the spectrum of a non~~-~~noetherian valuation ring.~~

	~~The definitions extend to~~ [~~[formal scheme]]s~~.

	~~== References ==~~
	* [[Robin Hartshorne]~~], ''Algebraic geometry''.~~






	~~{{geometry~~-~~stub}}~~

	[~~[Category~~:~~Algebraic geometry]~~]

en>TakuyaMurata: /* Definition */ here "any" means some

2013-12-26T02:12:14Z

Definition: here "any" means some

← Older revision		Revision as of 04:12, 26 December 2013
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	~~The writer~~'~~s name~~ is ~~Christy Brookins~~. ~~To play lacross~~ is ~~the thing I adore most~~ of ~~all~~. ~~Mississippi~~ is the only ~~place I~~'~~ve been residing in but I will have to move in~~ a ~~yr or two~~. ~~Distributing manufacturing is where her primary income arrives from~~.<br><br>~~Review my blog post~~ - ~~psychic phone (~~[~~http://www~~.~~khuplaza~~.~~com/dent/14869889 please click the next internet page~~])		In [[algebraic geometry]], a '''noetherian scheme''' is a [[scheme (mathematics)\|scheme]] that admits a finite covering by open affine subsets <math>\operatorname{Spec} A_i</math>, <math>A_i</math> [[noetherian rings]]. More generally, a scheme is '''locally noetherian''' if it is covered by spectra of noetherian rings. Thus, a scheme is noetherian if and only if it is locally noetherian and quasi-compact. As with noetherian rings, the concept is named after [[Emmy Noether]].

			It can be shown that, in a locally noetherian scheme, if  <math>\operatorname{Spec} A</math> is an open affine subset, then ''A'' is a noetherian ring. In particular, <math>\operatorname{Spec} A</math> is a noetherian scheme if and only if ''A'' is a noetherian ring. Let ''X'' be a locally noetherian scheme. Then the local rings <math>\mathcal{O}_{X, x}</math> are noetherian rings.

			A noetherian scheme is a [[noetherian topological space]]. But the converse is false in general; consider, for example, the spectrum of a non-noetherian valuation ring.

			The definitions extend to [[formal scheme]]s.

			== References ==
			* [[Robin Hartshorne]], ''Algebraic geometry''.






			{{geometry-stub}}

			[[Category:Algebraic geometry]]

en>ChuispastonBot: r2.7.1) (Robot: Adding he:העתקה רציונלית

2012-04-19T19:08:10Z

r2.7.1) (Robot: Adding he:העתקה רציונלית

New page

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