Attached primes and Artinian modules

Abstract

In this paper, we calculate the annihilator of an Artinian module over a complete local ring; moreover, we present a certain generalization of Grothendieck's Non-Vanishing Theorem for local cohomology modules over a local ring which is the homomorphic image of a Gorenstein local ring. Finally, as application of our results, we study the finiteness of local cohomology modules.