On the Matlis duals of local cohomology modules and modules of generalized fractions

Abstract

Let (R, m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with aM ≠ M. Let D(−) ≔ HomR(−, E) be the Matlis dual functor, where E ≔ E(R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x1, …, xn is a regular sequence on M contained in α, then H(x1, …,xnRnD(Han(M))) is a homomorphic image of D(M), where Hbi(−) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D(H(x1, …,xn)Rn(D(Han(M)))) ⋟ D(D(M)).