n. a module that satisfies the descending chain condition, so that every strictly descending (decreasing) chain of submodules is finite; this is equivalent to the satisfaction of the minimum condition. Every Artinian module is also a Noetherian module, but not necessarily vice versa; for example, the integers are a Noetherian but not an Artinian Z-module. (Named after Emil Artin (1898 - 1962), German-born American algebraist and group theorist.)