On pseudo supports and non-Cohen-Macaulay locus of finitely generated modules

Let (R, m) be a Noetherian local ring and M a finitely generated R-module with dim M = d. Let i >= 0 be an integer. Following M. Brodmann and R.Y. Sharp (2002) [BS1], the i-th pseudo support of M is the set of all prime ideals p of R such that H(pRp)(i-dim(R/p))(M(p)) not equal 0. In this paper, we study the pseudo supports and the non-Cohen-Macaulay locus of M in connections with the catenarity of the ring R/Ann(R) M, the Serre conditions on M, and the unmixedness of the local rings R/p for certain prime ideals p in Supp(R)(M). (C) 2010 Elsevier Inc. All rights reserved.