Tensor and Torsion Products of Relative Injective Modules with Respect to a Semidualizing Module

Abstract

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In this paper, we show that C is generically dualizing if and only if the tensor products of injective and C-injective R-modules are injective. This leads to a characterization of dualizing modules as well as generalizes a result of Enochs and Jenda.

Key Words:

• C-injective
• Dualizing
• Semidualizing

2010 Mathematics Subject Classification:

• 13D05
• 13D45
• 18G20

ACKNOWLEDGMENT

The authors wish to thank the anonymous referee for helpful suggestions.

Notes

Communicated by T. Albu.