17 мая 2022 г. · Definition 1. A commutative ring with unity A is Noetherian if and only if every ideal of A is finitely generated. Theorem · Proof

22 мар. 2013 г. · A ring satisfying any, and hence all three, of the above conditions is defined to be a left Noetherian ring. A right Noetherian ring is similarly defined.

Equivalently, a ring is left-Noetherian (respectively right-Noetherian) if every left ideal (respectively right-ideal) is finitely generated. A ring is ...

22 окт. 2015 г. · If every ascending chain of primary ideals in R stabilizes, is R a Noetherian ring? Equivalence of definitions of Noetherian Ring, another proof. Verifying three equivalent conditions for a ring to be Noetherian Equivalent definitions of Noetherian topological space Noetherian Ring under a Homomorphism / homomorphic ... Другие результаты с сайта math.stackexchange.com

18 июл. 2013 г. · Definition ; 1, ascending chain condition on ideals, any ascending chain of ideals stabilizes after a finite length ; 2, finite generation of ...

A ring is called left (respectively, right) Noetherian if it does not contain an infinite ascending chain of left (respectively, right) ideals.

14 нояб. 2023 г. · A commutative ring with unity A is Noetherian if and only if every ideal of A is finitely generated.

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.

Definition 1.1. A commutative ring R is called Noetherian if each ideal in R is finitely generated. This name honors Emmy Noether, who in her landmark ...

25 июл. 2024 г. · They're defined by the ascending chain condition on ideals, which means any chain of ideals eventually stops growing. This property has several ...