On the finiteness of the global dimension for Artinian rings (Q1614665)
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scientific article; zbMATH DE number 1797484
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the finiteness of the global dimension for Artinian rings |
scientific article; zbMATH DE number 1797484 |
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On the finiteness of the global dimension for Artinian rings (English)
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8 September 2002
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This short note contains the proof of the following result. Let \(A\) be a left Artinian ring. Suppose that each indecomposable finitely generated left \(A\)-module is of finite projective dimension or of finite injective dimension. Then \(A\) is of finite global dimension.
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homological dimension
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projective dimension
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injective dimension
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left Artinian rings
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indecomposable finitely generated modules
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