Module-relative-Hochschild (co)homology of tensor products

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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