CANONICAL ELEMENT CONJECTURE AND COHEN-MACAULAY RINGS

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.