Jump to content

Want site search autocompletion? See here
Encountering 429 Too Many Requests errors when browsing the site? See here

Toggle the table of contents

Noetherian ring

From Commalg

Revision as of 02:17, 9 January 2007 by Vipul (talk | contribs) (Started the page)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Definition for commutative rings

Symbol-free definition

A commutative unital ring is termed Noetherian if it satisfies the following equivalent conditions:

Ascending chain condition on ideals: Any ascending chain of ideals stabilizes after a finite length
Every ideal is finitely generated

Definition with symbols

Fill this in later

Definition for non-commutative rings

For non-commutative, there are two notions:

left Noetherian ring must satisfy the ascending chain condition on left ideals
right Noetherian ring must satisfy the ascending chain condition on right ideals

Retrieved from "https://commalg.subwiki.org/w/index.php?title=Noetherian_ring&oldid=842"

Properties of commutative rings