Endomorphism ring of local cohomology modules with respect to a pair of ideals

Author:

Talemi Atiyeh Pour Eshmanan1,Tehranian Abolfazl2

Affiliation:

1. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract

Let (R, 𝔪, k) be a complete Gorenstein local ring of dimension n. Let [Formula: see text] be the local cohomology module with respect to a pair of ideals I, J and [Formula: see text]. In this paper we will show that the endomorphism ring [Formula: see text] is a commutative ring. In particular if [Formula: see text] for all i ≠ t, then B is isomorphic to R. Also we prove that, B is a finite R-module if and only if [Formula: see text] is an Artinian R-module, where d = n - t. Moreover we will show that in the case that [Formula: see text] for all i ≠ t the natural homomorphism [Formula: see text] is nonzero which gives a positive answer to a conjecture due to Hellus–Schenzel (see [On cohomologically complete intersections, J. Algebra 320 (2008) 3733–3748]).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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