Tensor products of faithful modules

George M. Bergman

Tensor products of faithful modules

Rings and Algebras 2016-10-18 v1

Authors: George M. Bergman

Abstract

If $k$ is a field, $A$ and $B$ $k$ -algebras, $M$ a faithful left $A$ -module, and $N$ a faithful left $B$ -module, we recall the proof that the left $A\otimes_k B$ -module $M\otimes_k N$ is again faithful. If $k$ is a general commutative ring, we note some conditions on $A,$ $B,$ $M$ and $N$ that do, and others that do not, imply the same conclusion. Finally, we note a version of the main result that does not involve any algebra structures on $A$ and $B.$

Keywords

tensor product faithful module k-algebra commutative ring left module algebra structure

Cite

@article{arxiv.1610.05178,
  title  = {Tensor products of faithful modules},
  author = {George M. Bergman},
  journal= {arXiv preprint arXiv:1610.05178},
  year   = {2016}
}

Comments

4 pages. Copy at http://math.berkeley.edu/~gbergman/papers/unpub may be updated more frequently than arXiv copy

Tensor products of faithful modules

Abstract

Keywords

Cite

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