On Artinian generalized local cohomology modules

Abstract

Let R be a commutative Noetherian ring with non-zero identity and a be a maximal ideal of R. An R-module M is called minimax if there is a finitely generated submodule N of M such that M/N is Artinian. Over a Gorenstein local ring R of finite Krull dimension, we proved that the Socle of H (a) (n) (R) is a minimax R-module for each n a parts per thousand yen 0.