Finitely generated module

In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R-module also may be called a finite R-module,finite over R, or a module of finite type.

Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.