noetherian

Adjective

Meaning

(algebra) Of a ring in which any ascending chain of ideals eventually starts repeating.

(algebra) Of a module in which any ascending chain of submodules eventually starts repeating.

Noetherian (not comparable)

Alternative letter-case form of noetherian

Source: en.wiktionary.org

Phrases with the word

left Noetherian ring right Noetherian ring left-Noetherian right-Noetherian noetherian induction noetherian integral domain

Examples

Applications Let be a Noetherian commutative ring. Source: Internet

Bourbaki, 7.3, no 6, Proposition 4. The converse of this is not true: there are Noetherian local rings that are UFDs but whose completions are not. Source: Internet

A valuation ring is not Noetherian unless it is a principal ideal domain. Source: Internet

Another consequence is that a left Artinian ring is right Noetherian if and only if right Artinian. Source: Internet

Equivalent conditions for a ring to be a UFD A Noetherian integral domain is a UFD if and only if every height 1 prime ideal is principal (a proof is given below). Source: Internet

For a commutative ring to be Noetherian it suffices that every prime ideal of the ring is finitely generated. Source: Internet

Close letter words and terms

noes noesis Noether Noetherian domain noetherian induction noetherian integral domain