Noetherian ring
id:
noetherian-ring-293-8119372
title:
Noetherian ring
text:
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 I 1 ⊆ I 2 ⊆ I 3 ⊆ ⋯ of left ideals has a largest element; that is, there exists an n such that: I n = I n + 1 = ⋯ . Equivalently, a ring is left-Noetherian if every left ideal is finitely generated. A
brand slug:
wiki
category slug:
encyclopedia
description:
Mathematical ring with well-behaved ideals
original url:
https://en.wikipedia.org/wiki/Noetherian_ring
date created:
date modified:
2024-02-18T10:09:17Z
main entity:
{"identifier":"Q582271","url":"https://www.wikidata.org/entity/Q582271"}
image:
fields total:
13
integrity:
14