Artinian

Adjective

Meaning

(algebra, of a ring) in which any descending chain of ideals eventually starts repeating.

(algebra, of a module) in which any descending chain of submodules eventually starts repeating.

Source: en.wiktionary.org

Phrases with the word

Anagrams

Examples

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

If the module is Artinian, Noetherian, projective or injective, then the endomorphism ring has a unique maximal ideal, so that it is a local ring. Source: Internet

Conversely, every Artinian integral domain is a field. Source: Internet

The integers, however, form a Noetherian ring which is not Artinian. Source: Internet

It is a somewhat surprising fact that a left Artinian ring is left Noetherian (the Hopkins–Levitzki theorem ). Source: Internet

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