Faltings’ annihilator theorem and almost Cohen–Macaulay rings

Abstract

Faltings’ annihilator theorem is an important result in local cohomology theory. Recently, Doustimehr and Naghipour generalized the Falitings’ annihilator theorem. They proved that if [Formula: see text] is a homomorphic image of a Gorenstein ring, then [Formula: see text], where [Formula: see text] and [Formula: see text]. In this paper, we study the relation between [Formula: see text] and [Formula: see text], and prove that if [Formula: see text] is an almost Cohen–Macaulay ring, then [Formula: see text]. Using this result, we prove that if [Formula: see text] is a homomorphic image of a Cohen–Macaulay ring, then [Formula: see text].