A CHARACTERIZATION OF ALMOST DEDEKIND DOMAINS IN VIEW OF STRONG REPRESENTABILITY

Neda Pakyari; Esmaeil Rostami; Reza Nekooei

doi:10.1216/rmj.2023.53.897

Abstract

We show that an integral domain $R$ is an almost Dedekind domain if and only if $R$ is one-dimensional and every representable $R$ -module is strongly representable.

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Neda Pakyari. Esmaeil Rostami. Reza Nekooei. "A CHARACTERIZATION OF ALMOST DEDEKIND DOMAINS IN VIEW OF STRONG REPRESENTABILITY." Rocky Mountain J. Math. 53 (3) 897 - 902, June 2023. https://doi.org/10.1216/rmj.2023.53.897

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Received: 25 November 2021; Revised: 27 April 2022; Accepted: 15 August 2022; Published: June 2023

First available in Project Euclid: 21 July 2023

MathSciNet: MR4617919

zbMATH: 07731153

Digital Object Identifier: 10.1216/rmj.2023.53.897

Subjects:

Primary: 13F05

Secondary: 13C99

Keywords: almost Dedekind domain , representable module , secondary module , strongly representable module

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