(Weak) Gorenstein global dimension of semiartinian rings (Q555240)
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scientific article; zbMATH DE number 5931118
| Language | Label | Description | Also known as |
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| English | (Weak) Gorenstein global dimension of semiartinian rings |
scientific article; zbMATH DE number 5931118 |
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(Weak) Gorenstein global dimension of semiartinian rings (English)
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22 July 2011
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Summary: We prove that if \(R\) is a semiartinian commutative ring, the Gorenstein global dimension of \(R\) equals the supremum of the Gorenstein projective and injective dimensions of simple \(R\)-modules, and the weak Gorenstein global dimension of \(R\) equals the supremum of the Gorenstein flat dimensions of simple \(R\)-modules.
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simple modules
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projective modules
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projective dimension
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injective dimension
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flat dimension
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