Generalization of the Lichtenbaum–Hartshorne Vanishing Theorem: Communications in Algebra: Vol 40, No 1

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Abstract

In this article we shall prove the following result, which is a generalization of the Lichtenbaum–Hartshorne Vanishing Theorem (See [Citation3, Theorem 8.2.1]). Let (R, 𝔪) be a catenary Noetherian local ring, I an ideal of R and M be a nonzero finitely generated R-module of dimension n. Then the following conditions are equivalent: (i) and (ii) there exists a prime ideal 𝔭 in Assh_R(M) such that Rad(𝔭 +I) = 𝔪.

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2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

The authors are deeply grateful to the referee for his/her careful reading of the article and valuable suggestions.

This research of the authors was been supported by a grant from Islamic Azad University–Hashtroud branch.

Notes

Communicated by S. Goto.

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