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
Copyright © The Korean Mathematical Society.
Kui Hu, Hwankoo Kim, Dechuan Zhou
Southwest University of Science and Technology; Hoseo University; Southwest University of Science and Technology
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).
2019; 56(4): 1041-1057
2015; 52(1): 125-135
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