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 or finite over R.
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 related, finitely presented and coherent modules all coincide.
A finitely generated module over a field is simply a finite-dimensional vector space, and a finitely generated module over the integers is simply a finitely generated abelian group.
Read more about Finitely-generated Module: Formal Definition, Examples, Some Facts, Finitely Generated Modules Over A Commutative Ring, Equivalent Definitions and Finitely Cogenerated Modules, Finitely Presented, Finitely Related, and Coherent Modules