different between submodule vs noetherian

English

sub- +? module

submodule (plural submodules)

A module making up part of a larger module.
The first-year English Literature module consists of three submodules.
(algebra) A module contained in a larger module, both over the same ring, such that the ring multiplication in the former is a restriction of that in the latter.

From Emmy Noether

noetherian (not comparable)

(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.

Send