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arXiv · 1610.05178

Tensor products of faithful modules

George M. Bergman
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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 $B.$

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George M. Bergman. 2016-10-17. Tensor products of faithful modules. https://arxiv.org/abs/1610.05178

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