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.
2000 Mathematics Subject Classification:
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.