Abstract
Let R be a commutative Noetherian ring with non-zero identity, an ideal of R, M and X finite R–modules, and t a non-negative integer such that
is
–cofinite for all i < t. In this article, we show that
and
are finite, and
is finite if and only if
is finite. As a consequence, we observe that
is a finite set.
Acknowledgements
The authors would like to thank the referee for the invaluable comments on the manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.