Semi-local ring

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". 
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.