semi-local ring

A ring $R$ is semi-local if $R/rad(R)$ is an Artinian ring, where $rad(R)$ denotes the Jacobson radical of $R$. In the case that $R$ is commutative, this reduces to the definition that $R$ is semi-local if $R$ has finitely many maximal ideals. 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