## “School of Mathematics”

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Paper   IPM / M / 8869
 School of Mathematics Title: On the endomorphism rings of local cohomology modules Author(s): K. Khashyarmanesh Status: To Appear Journal: Canad. Math. Bull. Supported by: IPM
Abstract:
Let R be a commutative Noetherian ring and \mathfraka a proper ideal of R. We show that if n: = gradeR\mathfraka, then EndR(Hn\mathfraka(R)) ≅ ExtnR(Hn\mathfraka(R), R). We also prove that, for a non-negative integer n such that Hi\mathfraka(R) = 0 for every in, if ExtiR(Rz,R) = 0 for all i > 0 and z ∈ \mathfraka, then EndR(Hn\mathfraka(R)) is a homomorphic image of R, where Rz is the ring of fractions of R with respect to multiplicatively closed subset ⎣zj| j \geqslant 0 } of R. Also, if moreover HomR(Rz,R) = 0 for all z ∈ \mathfraka, then μ Hn\mathfraka(R) is isomorphism, where μHn\mathfraka(R) is the canonical ring homomorphism R → EndR(Hn\mathfraka(R)).