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

Abstract

Let (R,m) be a commutative Noetherian local ring with<br><br> non-zero identity, a a proper ideal of R and M a finitely<br><br> generated R-module with a M\\\\neq M. Let<br><br> D(-):=Hom_R(-,E) be the Matlis dual functor, where<br><br> E:=E(R/m) is the injective hull of the residue field R/m.<br><br>In this paper, by using a complex which involves modules of<br><br>generalized fractions, we show that, if x_1, ... ,x_n is a<br><br>regular sequence on<br><br> M contained in a, then H^n_(x_1, ... ,x_n)R<br><br> (D(H^n_a(M))) is a homomorphic image of D(M), where H^i_b(-) is<br><br>the i-th local cohomology functor with respect to an ideal<br><br>b of R. By applying this result, we study some conditions on<br><br>a certain module of generalized fractions under which<br><br>D(H^n_(x_1,... ,x_n)(D(H^n_a(M))))\\\\cong D(D(M)).