tailieunhanh - Some examples of the class of co-cohen-macaulay modules in dimension >s

In this paper, using the concept of A-cosequences in dimension > s introduced by [NH], we give some examples of the class of co-Cohen-Macaulay modules in dimension > s defined by [D3] in connection with some of the previous classes of modules. | Some examples of the class of co-Cohen-Macaulay modules in dimension >s Nguyen Thi Dung - Agriculture and Forestry University Abstract. In this paper, using the concept of A-cosequences in dimension > s introduced by [NH], we give some examples of the class of co-Cohen-Macaulay modules in dimension > s defined by [D3] in connection with some of the previous classes of modules. 1 Introduction Throughout this paper, let (R, m) be Noetherian local ring and A an Artinian R-module. The class of co-Cohen-Macaulay modules (co-CM for short) introduced by Tang and Zakeri [TZ] plays an important role in the catergory of Artinian modules. There are some classes of modules that contain the class co-CM modules, among which are co-filter modules and co-CM modules in dimension > s introduced by [D1], [D3] satisfying the condition that every system of parameters is a filter coregular sequence and a A-cosequence in dimension > s, respectively. Moreover, some properties and characterizations of these modules via systems of parameters, the dimension of the local homology modules Him (A) introduced by Cuong-Nam [CN], the polynomial type ld(A) of A given by Minh [MIN] and the multiplicity e(x; A) of A with respect to a . x defined by [CNh1] were given. The purpose of this paper is to give some examples of the class of co-CM modules in dimension > s defined by [D3] in the connection with some of the previous classes of modules. 2 Some examples Let s ≥ −1 be an integer. An A-cosequence in dimension > s was introduced in [NH] as an expansion of the notion of coregular sequence in [O]. Definition . A sequence (x1 , . . . , xk ) of elements in m is called an A-cosequence in dimension > s if xi ∈ / p for all attached primes p ∈ AttR (0 :A (x1 , . . . , xi−1 )R) satisfying dim(R/p) > s for all i = 1, . . . , k. Note that an A-cosequence in dimension > −1, 0 are exactly an A-cosequence in sense of A. Ooishi [O] and f-coregular sequence in sense of [D1], respectively. The .