Special Example of the Finite Dimension in Local Cohomology Modules

Abstract

Let, R be an total local ring, I an Ideal of R, and let M be a finitely generated R-module. Then H(M) Is I-cofinite in two cases. 1) I be a none zero principle Ideal. 2) I be a prime Ideal with dimension 1. In this paper we produce special example of the cofiniteness problem in local cohomology respect to a system of ideals. In fact we construct an ideal system with tridiagonal matrices of tridiagonal subsets which are true in the finite dimension in local cohomology modules.

Keywords: Local cohomology, Cofinite, Ideal system, Tridiagonal matrix