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 for left ideals or for right ideals, then the ring is said left-Noetherian or right-Noetherian respectively. That is, every increasing sequence. |
| Нётерово кольцо |  |
Нётерово кольцо́ — тип колец, обобщение кольца главных идеалов.
Названы в честь Эмми Нётер. Википедия
Noetherian Ring. A ring is called left (respectively, right) Noetherian if it does not contain an infinite ascending chain of left (respectively, right) ideals. |
But first we will prove that all proper ideals in. Noetherian rings have primary decompositions, and simplify the First Uniqueness Theorem. |
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 ... |
12 сент. 2024 г. · A Noetherian (or often, as below, noetherian) ring (or rng) is one where it is possible to do induction over its ideals, because the ordering of ... |
Noetherian ring, a ring that satisfies the ascending chain condition on ideals. ... Noetherian scheme, a scheme in algebraic geometry that admits a finite ... |
A ring R is Noetherian if any ideal of R is finitely generated. This is clearly equivalent to the ascending chain condition for ideals of R. By Lemma 10.28.10 ... |
3 апр. 2024 г. · An example of a Noetherian ring is any principal ideal ring, ie a ring in which every ideal has one generator. |
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