Abstract. Let R be a commutative Noetherian ring and a a proper ideal of R. We show that if n := gradeR a, then EndR(Hn a (R)) ∼ = Ext n R(Hn a (R), R). We also prove that, for a nonnegative integer n such that Hi a(R) = 0 for every i 6= n, if Ext i R(Rz , R) = 0 for all i > 0 and z ∈ a, then EndR(Hn a (R)) is a homomorphic image of R, where Rz is the ring of fractions of R with respect to a multiplicatively closed subset {z j | j > 0} of R. Moreover, if HomR(Rz , R) = 0 for all z ∈ a, then ¹Hn a (R) is an isomorphism, where ¹Hn a (R) is the canonical ring homomorphism R → EndR(Hn a (R))

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