WEAKLY LASKERIAN, WEAKLY COFINITE MODULES AND GENERALIZED LOCAL COHOMOLOGY

Abstract

Let R be a commutative Noetheran ring, I an ideal of R and M be a finitely generated projective R-module. Let N be an R module and t a non-negative integer such that Extt R(M/IM, N) is weakly Laskerian. Then for any weakly Laskerian submodule U of the first non I-weakly cofinite module HtI(M, N), the R-module HomR(M/IM, HtI(M, N)/U) is weakly Laskerian. As a consequence the set of associated primes of HtI(M, N)/U is finite.