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Module-relative-Hochschild (co)homology of tensor products |
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| Authors: | Yuan Chen |
| Affiliation: | 1. School of Mathematics and Computer Science, Hubei University, Wuhan 430062, China; 2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
| Abstract: | In this paper, we consider the module-relative-Hochschild homology and cohomology of tensor products of algebras and relate them to those of the factor algebras. Moreover, we show that the tensor product is formally smooth if and only if one of its factor algebras is formally smooth and the other is separable. |
| Keywords: | Tensor product module-relative-Hochschild (co)homology formal smoothness |
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