2020/04/05 by Marco D’Anna, D'Anna, Marco, Francesco Strazzanti +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2004.02252
openalex publication_date 2020/04/05 · openalex created_date 2020/04/10 · openalex updated_date 2026/07/28
Given a one-dimensional Cohen-Macaulay local ring (R,\mathfrakm,k), we prove that it is almost Gorenstein if and only if \mathfrakm is a canonical module of the ring \mathfrakm:\mathfrakm. Then, we generalize this result by introducing the notions of almost canonical ideal and gAGL ring and by proving that R is gAGL if and only if \mathfrakm is an almost canonical ideal of \mathfrakm:\mathfrakm. We use this fact to characterize when the ring \mathfrakm:\mathfrakm is almost Gorenstein, provided that R has minimal multiplicity. This is a generalization of a result proved by Chau, Goto, Kumashiro, and Matsuoka in the case in which \mathfrakm:\mathfrakm is local and its residue field is isomorphic to k.