Associated Primes and Syzygies of Linked Modules

Authors

Olgur Celikbas, West Virginia UniversityFollow
Mohammad T. Dibaei, Kharazmi UniversityFollow
Mohsen Gheibi, University of Nebraska - LincolnFollow
Arash Sadeghi, Institute for Research in Fundamental SciencesFollow
Ryo Takahaski, University of Nebraska-Lincoln and Nagoya UniversityFollow

Date of this Version

2019

Citation

J. Commut. Alegbra Forthcoming (2019).

Comments

CELIKBAS, DIBAEI, GHEIBI, SADEGHI, TAKAHASHI

Abstract

Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring R, if a Cohen-Macaulay R-module M of grade g is linked to an R-module N by a Gorenstein ideal c, such that AssR(M)\AssR(N) = ;, then M R N is isomorphic to direct sum of copies of R=a, where a is a Gorenstein ideal of R of grade g + 1. We give a criterion for the depth of a local ring (R;m; k) in terms of the homological dimensions of the modules linked to the syzygies of the residue eld k. As a result we characterize a local ring (R;m; k) in terms of the homological dimensions of the modules linked to the syzygies of k.