ON SOME PROPERTIES OF THE PSEUDO SUPPORT IN DIMENSION MORE THAN S

Abstract

Let (R, m) be a Noetherian local ring and M be a finitely generated Rmodule. Let s and i be integers such that i ≥ 0 and s ≥ −1. The i-th pseudo support in dimension more than s of M, denoted by PsuppiR(M) >s, is defined by PsuppiR(M) >s = {p ∈ Spec R | N-dimRp Hpi −Rdimp R/ p(Mp) > s}. The i-th pseudo support in dimension more than −1 of M is the i-th pseudo support of M introduced by Markus Brodmann and R. Y. Sharp, the i-th pseudo support in dimension more than 0 of M is the i-th length support of M introduced by Le Thanh Nhan, Nguyen Thi Kieu Nga and Pham Huu Khanh (2014). They are useful tools in studying Cohen-Macaulay loci. In this paper, we are going to present some properties of the i-th pseudo support in dimension more than s of M.