An elementary proof of Nagel-Schenzel formula

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University (PNU), P.O.BOX, 19395-4697, Tehran, Iran

Abstract

Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R--module, and a1,,an an a--filter regular M--sequence. The formula
Hai(M){H(a1,,an)i(M)for all i<n,Hain(H(a1,,an)n(M))for all in,
is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.

Keywords


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