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SOME ONE-DIMENSIONAL NOETHERIAN DOMAINS AND G-PROJECTIVE MODULES

김환구|Kui Hu|De Chuan Zhou
대한수학회 (The Korean Mathematical Society)|2023.11|대한수학회보 (Bulletin of the KMS)|제60권 제6호|pp. 1453-1461|DOI 10.4134/BKMS.b220513

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참고문헌

키워드

$G$-projective moduleone-dimensional Noetherian domainreflexive moduledivisorial ideal
주제분류수학

초록

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.

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.

참고문헌 (18)

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