Tensor products of faithful modules
Skip to main content
Open Access Publications from the University of California

Tensor products of faithful modules

  • Author(s): Bergman, George M
  • et al.

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 $B.$

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View