Tensor products of faithful modules

2016/10/17 by George M. Bergman, Bergman, George M. · 1 citation
Mathematics · #16S99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary: 16D10 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16D10 #msc:16S99

paper · pdf · doi:10.48550/arxiv.1610.05178

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

arxiv created 2016/10/17 · openalex publication_date 2016/10/17 · arxiv updated 2016/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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⊗_k B-module M⊗_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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