Some one-dimensional Noetherian domains and G-projective modules

Kui Hu; Hwankoo Kim; Dechuan Zhou

doi:10.4134/BKMS.b220513

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(6): 1453-1461

Online first article November 17, 2023 Printed November 30, 2023

https://doi.org/10.4134/BKMS.b220513

Some one-dimensional Noetherian domains and G-projective modules

Kui Hu, Hwankoo Kim, Dechuan Zhou

Southwest University of Science and Technology; Hoseo University; Southwest University of Science and Technology

Abstract

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Abstract

Let $R$ be a one-dimensional Noetherian domain with quotient field $K$ and $T$ be the integral closure of $R$ in $K$. In this note we prove that if the conductor ideal $(R:_KT)$ is a nonzero prime ideal, then every finitely generated reflexive (and hence finitely generated $G$-projective) $R$-module is isomorphic to a direct sum of some ideals.

Keywords: $G$-projective module, one-dimensional Noetherian domain, reflexive module, divisorial ideal

MSC numbers: Primary 13G05, 13D03

Supported by: The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2021R1I1A3047469). The third author was supported by National Natural Science Foundation of China (12101515).