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.
"Attached primes and Artinian modules." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 63 - 70, march 2018. https://doi.org/10.36045/bbms/1523412053