Let S be a ring with subring R.

We say that S is module-finite over R if S is finitely generatedMathworldPlanetmathPlanetmath as an R-module.

We say that S is ring-finite over R if S=R[v1,,vn] for some v1,,vnS.

Note that module-finite implies ring-finite, but the converse is false.

If L is ring-finite over K, with L,K fields, then L is a finite extensionMathworldPlanetmath of K.

Title module-finite
Canonical name Modulefinite
Date of creation 2013-03-22 12:36:56
Last modified on 2013-03-22 12:36:56
Owner yark (2760)
Last modified by yark (2760)
Numerical id 6
Author yark (2760)
Entry type Definition
Classification msc 13B02
Classification msc 13C05
Classification msc 16D10
Related topic FinitelyGeneratedRModule
Defines ring-finite