2023/12/22 by Naoki Endo, Endo, Naoki
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.2312.14379
openalex publication_date 2023/12/22 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28
As part of stratification of Cohen-Macaulay rings, we introduce and develop the theory of Goto rings, generalizing the notion of almost Gorenstein rings originally defined by V. Barucci and R. Fröberg in 1997. What has dominated the series of researches on almost Gorenstein rings is the fact that the reduction numbers of extended canonical ideals are at most 2; we define Goto rings as Cohen-Macaulay rings admitting such extended canonical ideals. We provide a characterization of Goto rings in terms of the structure of Sally modules and determine the Hilbert functions of them. Various examples of Goto rings that come from numerical semigroups, idealizations, fiber products, and equimultiple Ulrich ideals are explored as well.