Projective modules with semilocal endomorphism ring. (Q1397533)
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scientific article; zbMATH DE number 1960487
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Projective modules with semilocal endomorphism ring. |
scientific article; zbMATH DE number 1960487 |
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Projective modules with semilocal endomorphism ring. (English)
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11 August 2003
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Let \(R\) be an associative ring with identity element. The authors prove that a projective left \(R\)-module \(P\), whose ring of endomorphisms is semilocal, is finitely generated if and only if the dual Goldie dimensions of \(P\) and of the factor module \(P/J(P)\) of \(P\) by its Jacobson radical \(J(P)\) are equal.
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projective modules
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semilocal rings
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dual Goldie dimension
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