semi-local ring

A ring R is semi-local if R/rad(R) is an Artinian ring, where rad(R) denotes the Jacobson radicalMathworldPlanetmath of R. In the case that R is commutativePlanetmathPlanetmathPlanetmath, this reduces to the definition that R is semi-local if R has finitely many maximal idealsMathworldPlanetmath. Note that finite rings are trivially semi-local.

Title semi-local ring
Canonical name SemilocalRing
Date of creation 2013-03-22 12:56:42
Last modified on 2013-03-22 12:56:42
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Definition
Classification msc 16L30
Classification msc 13H99
Synonym semilocal ring
Related topic LocalRing