Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 3: 415 - 426

DOI: https://doi.org/10.1007/s11464-012-0200-y

RESEARCH ARTICLE

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

  • Yuan CHEN , 1,2
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  • 1. School of Mathematics and Computer Science, Hubei University, Wuhan 430062, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received date: 03 Jun 2011

Accepted date: 20 Feb 2012

Published date: 01 Jun 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Tensor product; module-relative-Hochschild (co)homology; formal smoothness

Cite this article

Yuan CHEN . Module-relative-Hochschild (co)homology of tensor products[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 415 -426 . DOI: 10.1007/s11464-012-0200-y

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