CANONICAL ELEMENT CONJECTURE AND COHEN-MACAULAY RINGS

Print ISSN: 2319-1023 | Online ISSN: 2582-5461

Abstract

Let M be a module over a commutative Noetherian ring A and J be an ideal of A. In this short note, it is proved, by an elementary argument, that if $x_1,...,x_n$ is an M-sequence contained in J, then $Hom_A(A/J,H_J^n(M))\cong (x_1,...,x_n)M:_{M}J/(x_1,...,x_n)M$. As an application of this result, the canonical element conjecture is established in a certain case.

Keywords and Phrases

Cohen-Macaulay ring, Canonical Element Conjecture, local cohomology, maximal Cohen-Macaulay module.

A.M.S. subject classification

14B15, 13E05, 13D45.

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