# GENERALIZED LOCAL COHOMOLOGY AND MATLIS DUALITY

• Abbasi, Ahmad (Department of Mathematics, Faculty of Sciences, University of Guilan)
• Accepted : 2008.08.25
• Published : 2008.09.25
• 58 6

#### Abstract

Let (R, m) be a Noetherian local ring with maximal ideal m, E := $E_R$(R/m) and let I be an ideal of R. Let M and N be finitely generated R-modules. It is shown that $H^n_I(M,(H^n_I(N)^{\vee})){\cong}(M{\otimes}_RN)^{\vee}$ where grade(I, N) = n = $cd_i$(I, N). We also show that for n = grade(I, R), one has $End_R(H^n_I(P,R)^{\vee}){\cong}Ext^n_R(H^n_I(P,R),P^*)^{\vee}$.

#### Keywords

Generalized local cohomology;Local cohomology;Matlis duality

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