# 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 SemilocalRing 2013-03-22 12:56:42 2013-03-22 12:56:42 mathcam (2727) mathcam (2727) 7 mathcam (2727) Definition msc 16L30 msc 13H99 semilocal ring LocalRing