In mathematics, a **semi-local ring** is a ring for which *R*/J(*R*) is a semisimple ring, where J(*R*) is the Jacobson radical of *R*. (Lam 2001, §20)(Mikhalev 2002, C.7)

The above definition is satisfied if *R* has a finite number of maximal right ideals (and finite number of maximal left ideals). When *R* is a commutative ring, the converse implication is also true, and so the definition of semi-local for commutative rings is often taken to be "having finitely many maximal ideals".

Some literature refers to a commutative semi-local ring in general as a *quasi-semi-local ring*, using semi-local ring to refer to a Noetherian ring with finitely many maximal ideals.

A semi-local ring is thus more general than a local ring, which has only one maximal (right/left/two-sided) ideal.