A Canonical module characterization of Serre's $(\mathrm{R}_1)$

Lukas Katthän; Kohji Yanagawa

A Canonical module characterization of Serre's $(\mathrm{R}_1)$

Commutative Algebra 2016-01-20 v2

Authors: Lukas Katthän , Kohji Yanagawa

Abstract

In this short note, we give a characterization of domains satisfying Serre's condition $(\mathrm{R}_1)$ in terms of their canonical modules. In the special case of toric rings, this generalizes a result of the second author (K. Yanagawa, Dualizing complexes of seminormal affine semigroup rings and toric face rings, J. Algebra 425 (2015).) where the normality is described in terms of the "shape" of the canonical module.

Keywords

module theory commutative algebra commutative ring theory

Cite

@article{arxiv.1506.02537,
  title  = {A Canonical module characterization of Serre's $(\mathrm{R}_1)$},
  author = {Lukas Katthän and Kohji Yanagawa},
  journal= {arXiv preprint arXiv:1506.02537},
  year   = {2016}
}

Comments

6 pages. Shortened exposition and improved Theorem 4.2. To appear in Comm. Alg

A Canonical module characterization of Serre's $(\mathrm{R}_1)$

Abstract

Keywords

Cite

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