On the finiteness of associated primes of local cohomology modules

Abstract

Abstract: Let $ R $ be a Noetherian ring, $\ mathfrak {a} $ be an ideal of $ R $ and $ M $ be a finitely generated $ R $-module. The aim of this paper is to show that if $ t $ is the least integer such that neither $ H^ t_ {\ mathfrak {a}}(M) $ nor ${supp}(H^ t_ {\ mathfrak {a}}(M)) $ is non-finite, then $ H^ t_ {\ mathfrak {a}}(M) $ has finitely many associated primes. This combines the main results of Brodmann and Faghani and independently of Khashyarmanesh and Salarian.