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". A semi-local ring is thus more general than a local ring, which has only one maximal (right/left/two-sided) ideal.
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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". A semi-local ring is thus more general than a local ring, which has only one maximal (right/left/two-sided) ideal.
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In mathematics, a semi-local r ...... (right/left/two-sided) ideal.
@en
数学において、半局所環 (semi-local ring) ...... 両側)イデアルをただひとつだけもつ局所環よりも一般的である。
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In mathematics, a semi-local r ...... (right/left/two-sided) ideal.
@en
数学において、半局所環 (semi-local ring) ...... 両側)イデアルをただひとつだけもつ局所環よりも一般的である。
@ja
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Semi-local ring
@en
半局所環
@ja