When is a flat module projective (Q794748)
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scientific article; zbMATH DE number 3859339
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When is a flat module projective |
scientific article; zbMATH DE number 3859339 |
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When is a flat module projective (English)
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1984
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The author proves the following Theorem: Let \(R\subset S\) be an extension of rings. Let M be a flat left R-module. For M to be projective, it is necessary and sufficient that there exists an exact sequence \(0\to K\to P\to M\to 0\) of left R-modules with P projective and the scalar extension \(S\otimes_ RK\) a finitely generated left S-module.
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extension
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flat left R-module
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exact sequence
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