Tensor product of injective modules

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Are tensor products of injective modules always injective?

There is a question[1] on Math.Stackexchange asking this. Under it, a post provides two refrences for general criteria:

  • Ishikawa, Takeshi. “On injective modules and flat modules.” Journal of the Mathematical Society of Japan 17.3 (1965): 291-296.
  • Enochs, Edgar E., and Overtoun MG Jenda. “Tensor and torsion products of injective modules.” Journal of Pure and Applied Algebra 76.2 (1991): 143-149.

Here I give an example:

R=K[x,y]/(x2,xy,y2),M=(x,y).R=K[x,y]/(x^2,xy,y^2), M=(x,y).

  1. http://math.stackexchange.com/questions/623907/is-it-true-that-tensor-product-of-injective-modules-is-injective ↩︎