Spring 2023 TORSION-FREE EXTENSIONS OF PROJECTIVE MODULES BY TORSION MODULES
László Fuchs
J. Commut. Algebra 15(1): 31-44 (Spring 2023). DOI: 10.1216/jca.2023.15.31

Abstract

We consider a generalization of a problem raised by P. Griffith on abelian groups to modules over integral domains, and prove an analogue of a theorem of M. Dugas and J. Irwin. Torsion modules T with the following property are characterized: if M is a torsion-free module and F is a projective submodule such that MFT, then M is projective. It is shown that for abelian groups whose cardinality is not cofinal with ω this is equivalent to being totally reduced in the sense of L. Fuchs and K. Rangaswamy. The problem for valuation domains is also discussed, with results similar to the case of abelian groups.

Citation

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László Fuchs. "TORSION-FREE EXTENSIONS OF PROJECTIVE MODULES BY TORSION MODULES." J. Commut. Algebra 15 (1) 31 - 44, Spring 2023. https://doi.org/10.1216/jca.2023.15.31

Information

Received: 1 July 2021; Revised: 3 August 2021; Accepted: 3 August 2021; Published: Spring 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604783
zbMATH: 07725172
Digital Object Identifier: 10.1216/jca.2023.15.31

Subjects:
Primary: 13C12
Secondary: 13F30 , 13G05 , 20K10

Keywords: abelian p-group , critical filtration , tight submodule , torsion , uniserial module , Valuation domain

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.15 • No. 1 • Spring 2023
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