FINITENESS PROPERTIES OF LOCAL COHOMOLOGY MODULES FOR (I, J)-MINIMAX MODULES

Let R be a commutative noetherian ring and let I and J be two ideals of R. In this paper, we introduce the concept of (I, J)-minimax R-module and it is shown that if M is an (I, J)-minimax R-module and t a non-negative integer such that Hi I,J (M) is (I, J)-minimax for all i t, then for any (I, J)- minimax submodule N of Ht I,J (M), the R-module HomR(R / I, Ht I,J (M) / N) is (I, J)-minimax. As a consequence, it follows that the Goldie dimension of Ht I,J (M) / N is finite and so the set of associated primes of Ht I,J (M) / N is finite. This generalizes the main result of Azami, Naghipour and Vakili [2, Theorem 4.2].