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2019 Associated primes and syzygies of linked modules
Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahashi
J. Commut. Algebra 11(3): 301-323 (2019). DOI: 10.1216/JCA-2019-11-3-301

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 $\mathrm {Ass}_R(M)$ and $\mathrm {Ass}_R(N)$ are disjoint, then $M\otimes _RN$ is isomorphic to direct sum of copies of $R/\mathfrak {a}$, where $\mathfrak {a}$ is a Gorenstein ideal of $R$ of grade $g+1$. We give a criterion for the depth of a local ring $(R,\mathfrak {m},k)$ in terms of the homological dimensions of the modules linked to the syzygies of the residue field $k$. As a result we characterize a local ring $(R,\mathfrak {m},k)$ in terms of the homological dimensions of the modules linked to the syzygies of $k$.

Citation

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Olgur Celikbas. Mohammad T. Dibaei. Mohsen Gheibi. Arash Sadeghi. Ryo Takahashi. "Associated primes and syzygies of linked modules." J. Commut. Algebra 11 (3) 301 - 323, 2019. https://doi.org/10.1216/JCA-2019-11-3-301

Information

Published: 2019
First available in Project Euclid: 3 December 2019

zbMATH: 07140749
MathSciNet: MR4038052
Digital Object Identifier: 10.1216/JCA-2019-11-3-301

Subjects:
Primary: 13D07
Secondary: 13C40, 13D02, 13D05

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.11 • No. 3 • 2019
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