Noetherian ring:Noetherian
Noetherian
Noetherianring,aringthatsatisfiestheascendingchainconditiononideals....Noetherianscheme,aschemeinalgebraicgeometrythatadmitsafinite ...。其他文章還包含有:「4.4NoetherianRings」、「6.4.ExamplesofNoetherianrings.Sofartheonly...」、「GeneralRingTheoryNoetherianrings」、「Hilbert'sbasistheorem」、「Noetherianring」、「NoetherianRing」、「noetherianringinnLab」、「NoetherianRing:MostUp-to」、...
查看更多 離開網站4.4 Noetherian Rings
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But first we will prove that all proper ideals in. Noetherian rings have primary decompositions, and simplify the First Uniqueness Theorem.
6.4. Examples of Noetherian rings. So far the only ...
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So far the only rings we can easily prove are Noetherian are principal ideal domains, like Z and k[x], or finite. Our goal now is to develop theorems that ...
General Ring TheoryNoetherian rings
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We will state and prove results only for right-noetherian rings, even though they are valid mutatis mutandis for left-noetherian and noetherian rings just as ...
Hilbert's basis theorem
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In mathematics, specifically commutative algebra, Hilbert's basis theorem says that a polynomial ring over a Noetherian ring is Noetherian.
Noetherian ring
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In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only ...
Noetherian Ring
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A ring is called left (respectively, right) Noetherian if it does not contain an infinite ascending chain of left (respectively, right) ideals.
noetherian ring in nLab
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A ring R R is Noetherian if it satisfies the ascending chain condition on its two-sided ideals: for every ascending chain of two-sided ideals ( ...
Noetherian Ring: Most Up-to
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A ring is a Noetherian ring if it is both left Noetherian and right Noetherian. For commutative rings, all three concepts are the same, but in general they are ...
NOETHERIAN RINGS 1. Introduction In a PID
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A commutative ring R is called Noetherian if each ideal in R is finitely generated. This name honors Emmy Noether, who in her landmark paper [6] in 1921 proved ...