Test Modules for Projectivity of Duals

Abstract

Over a regular local ring R, given a nonzero R-module N and an arbitrary R-module M, we examine conditions for the freeness of the dual M*, in terms of vanishing of the groups, .

Key Words:

• Depth
• Duals
• Projective dimension
• Regular local rings

2000 Mathematics Subject Classification:

• Primary 13C10, 13D05
• Secondary 13H05

ACKNOWLEDGMENT

The authors thank the referee for suggesting modifications in the presentation of the results of our article. The statement of Remark 2 is a generalization of one of our results in the earlier version, and the possibility was suggested by the referee.

Notes

Communicated by A. Singh.