On the cofiniteness of Artinian local cohomology modules

摘要

Let (R, m) be a commutative Noetherian local ring, which is a homomorphic image of a Gorenstein local ring and I an ideal of R. Let M be a nonzero finitely generated R-module and i >= 0 be an integer. In this paper we show that, the R-module H-m(i) (M) is nonzero and I-cofinite if and only if Rad(I+0 :(R) H-m(i) (M)) = m. Also, several applications of this result will be included.

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