On the tensor product of algebras (Q2818762)
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scientific article; zbMATH DE number 6625229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the tensor product of algebras |
scientific article; zbMATH DE number 6625229 |
Statements
8 September 2016
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tensor product of \(k\)-algebras
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regular ring
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complete intersection ring
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Gorenstein ring
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Cohen-Macaulay ring
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Noetherian ring
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separable extension
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On the tensor product of algebras (English)
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This paper is concerned with the study of the structure of the tensor product of algebras over a fields.NEWLINENEWLINEHis aim is to show: {Let \(\sigma: A \rightarrow B\) and \(\rho: A \rightarrow C\) be two homomorphisms of noetherian rings such that \(B\otimes_{A}C\) is a noetherian ring. Then if \(\sigma\) is a regular (resp. complete intersection, resp. Gorentein, resp. Cohen-Macaulay, resp. (\(S_{n}\))), resp. almost Cohen-Macaulay) homomorphism, so is \(\sigma \otimes I_{C}\)}.NEWLINENEWLINEThe paper was ended by the transfer of the previous properties of \(B\) and \(C\) to \(B\otimes_{A} C\) and then to the completed tensor product \(\widehat{B\otimes_{A} C}\).
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