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SOME CHARACTERIZATIONS OF COHEN-MACAULAY MODULES IN DIMENSION > s

  • Dung, Nguyen Thi
  • Received : 2012.12.20
  • Published : 2014.03.31

Abstract

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. For an integer s > -1, we say that M is Cohen-Macaulay in dimension > s if every system of parameters of M is an M-sequence in dimension > s introduced by Brodmann-Nhan [1]. In this paper, we give some characterizations for Cohen-Macaulay modules in dimension > s in terms of the Noetherian dimension of the local cohomology modules $H^i_m(M)$, the polynomial type of M introduced by Cuong [5] and the multiplicity e($\underline{x}$;M) of M with respect to a system of parameters $\underline{x}$.

Keywords

Cohen-Macaulay modules in dimension > s;M-sequence in dimension > s;multiplicity;Noetherian dimension;local cohomology modules

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