Page "Nakayama lemma" Paragraph 17

In the special case of a finitely generated module M over a local ring R with maximal ideal m, the quotient M / mM is a vector space over the field R / m.

Statement 4 then implies that a basis of M / mM lifts to a minimal set of generators of M. Conversely, every minimal set of generators of M is obtained in this way, and any two such sets of generators are related by an invertible matrix with entries in the ring.