Injective and flat dimensions. II (Q1111624)
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scientific article; zbMATH DE number 4075244
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Injective and flat dimensions. II |
scientific article; zbMATH DE number 4075244 |
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Injective and flat dimensions. II (English)
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1989
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[For part I see Math. Jap. 31, 205-209 (1986; Zbl 0593.13008).] In this paper, we show that if R is a commutative noetherian ring of finite global dimension, then gl.dim(R)\(\leq n\) if and only if for each injective R-module E, id(M\(\otimes E)\leq n-2\) for all R-modules M and equivalently for each injective R-module E, fd(Hom(E,M))\(\leq n-2\) for all R-modules M.
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finite global dimension
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flat dimension
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precover
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injective dimension
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