Semi-local ring

（重定向自Semilocal 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. (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".

单词	Semilocal ring
释义	Semilocal ring 英语百科 Semi-local ring （重定向自Semilocal 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. (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".
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