Duality for a Cohen–Macaulay Local Ring

Abstract

Let (R, 𝔪) be a Cohen–Macaulay local ring. If R has a canonical module, then there are some interesting results about duality for this situation. In this article, we show that one can indeed obtain similar results in the case R does not have a canonical module. Also, we give some characterizations of complete big Cohen–Macaulay modules of finite injective dimension, and by using them, some characterizations of Gorenstein modules over the 𝔪-adic completion of R are obtained.

Key Words:

• Balanced big Cohen–Macaulay module
• Canonical module
• Cohen–Macaulay local ring
• Complete module
• Cousin complex

2000 Mathematics Subject Classification:

• Primary 13C14, 13J10
• Secondary 13D05, 13C13

ACKNOWLEDGMENT

We would like to thank the referee for his/her useful suggestion.

This research was in part supported by a grant from IPM (No. 87130214).

Notes

Communicated by I. Swanson.