Editing Noetherian module (section)

In [[abstract algebra]], a '''Noetherian module''' is a [[module (mathematics)|module]] that satisfies the [[ascending chain condition]] on its [[submodule]]s, where the submodules are [[partially ordered]] by [[inclusion (set theory)|inclusion]].<ref>{{harvnb|Roman|2008|loc=p. 133 §5}}</ref>

Historically, [[David Hilbert|Hilbert]] was the first mathematician to work with the properties of [[finitely generated module|finitely generated submodules]]. He [[mathematical proof|proved]] an important theorem known as [[Hilbert's basis theorem]] which says that any [[ideal (ring theory)|ideal]] in the multivariate [[polynomial ring]] of an arbitrary [[field (mathematics)|field]] is [[Ideal (ring theory)#Types of ideals|finitely generated]]. However, the property is named after [[Emmy Noether]] who was the first one to discover the true importance of the property.