Faltings' theorem for the annihilation of local cohomology modules over a Gorenstein ring

In this paper we study the Annihilator Theorem and the Local-global Principle for the annihilation of local cohomology modules over a (not necessarily finite-dimensional) Noetherian Gorenstein ring.

     

Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules

Let R be a commutative Noetherian ring, be an ideal of R and M be a finitely generated R-module. Melkersson and Schenzel asked whether the set becomes stable for a fixed integer i and sufficiently large j. This paper is concerned with this question. In fact, we prove that if s ≥ 0 and n ≥ 0 such that for all i with i < n, then is finite for all i with i < n, and is finite for all i with i ≤ n, where for a subset T of Spec(R), we set . Also, among other things, we show that if n ≥ 0, R is semi-local and is finite for all i with i < n, then is finite for all i with i ≤ n. K. Khashyarmanesh was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran (No. 86130027).     

The strong persistence property and symbolic strong persistence property

Czechoslovak Mathematical Journal - Let I be an ideal in a commutative Noetherian ring R. Then the ideal I has the strong persistence property if and only if (Ik+1: RI) = Ik for all k, and I has...     

Planar zero divisor graphs of partially ordered sets

We associate a graph G ^?(P) to a partially ordered set (poset, briefly) with the least element?0, as an undirected graph with vertex set P ^?=P?{0} and, for two distinct vertices x and y, x is adjacent to?y in?G ^?(P) if and only if {x,y} ^? ={0}, where, for a subset?S of?P, S ^? is the set of all elements x∈P with x≦s for all s∈S. We study some basic properties of?G ^?(P). Also, we completely investigate the planarity of?G ^?(P).