ABSTRACT
Let (R,𝔪) be a complete noetherian local ring and M a finitely generated R-module of dimension n and 𝔞 an ideal of R.
At first, we find a relation between top local cohomology and top formal local cohomology modules. In fact, we show that there exists an ideal 𝔟 such that and there exists an ideal 𝔠 such that . Several applications of this result are given. Among other things, it is shown that and .
Acknowledgment
The author would like to thank the referee for his/her useful suggestions.