Journal•ISSN: 1939-2346
Journal of Commutative Algebra
Rocky Mountain Mathematics Consortium
About: Journal of Commutative Algebra is an academic journal published by Rocky Mountain Mathematics Consortium. The journal publishes majorly in the area(s): Local ring & Monomial. It has an ISSN identifier of 1939-2346. Over the lifetime, 314 publications have been published receiving 2852 citations. The journal is also known as: JCA.
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286 citations
TL;DR: In this article, it was shown that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded by the length of its longest induced path and bounded above by the number of its vertices.
Abstract: We show that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.
99 citations
TL;DR: The notion of projective modules over non-noetherian commutative rings was introduced and investigated in this article, where a semidualizing projective module is considered.
Abstract: We introduce and investigate the notion of $\gc$-projective modules over (possibly non-noetherian) commutative rings, where $C$ is a semidualizing module. This extends Holm and J{\o}rgensen's notion of $C$-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite $\gc$-projective dimension, showing in particular that they admit $\gc$-projective approximations, a generalization of the maximal Cohen-Macaulay approximations of Auslander and Buchweitz. Over a local (noetherian) ring, we provide necessary and sufficient conditions for a $G_C$-approximation to be minimal.
87 citations
86 citations
TL;DR: In this paper, the notion of duality pair was introduced and it was shown that the left half of such a pair is often covering and preenveloping, whereas the right half of the pair is not often covering.
Abstract: We introduce the notion of a duality pair and demonstrate how the left half of such a pair is “often” covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules—introduced by Enochs and Jenda—is covering when the ground ring has a dualizing complex.
83 citations