CANONICAL ELEMENT CONJECTURE AND COHEN-MACAULAY RINGS
Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 86
DOI:
Author :
Mohammad Amin Raeisi Makiani (Department of Mathematical Sciences, Kharazmi University, No. 599, Taleghani Ave., Tehran, IRAN)
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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