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April 2021 Cancellation and stability properties of generalized torsion modules
F. E. A. Johnson
Rocky Mountain J. Math. 51(2): 585-591 (April 2021). DOI: 10.1216/rmj.2021.51.585

Abstract

Given a module X over a ring Λ its stability class consists of all modules X such that XΛaXΛb for some positive integers a, b. If the ring Λ is weakly finite then the stability class of a finitely generated Λ-module has the structure of a tree. We show that if, in addition, X is a generalized torsion module its stability class has the same shape as that of the zero module. In consequence we construct examples of nonprojective modules whose stability classes have arbitrarily large amounts of branching.

Citation

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F. E. A. Johnson. "Cancellation and stability properties of generalized torsion modules." Rocky Mountain J. Math. 51 (2) 585 - 591, April 2021. https://doi.org/10.1216/rmj.2021.51.585

Information

Received: 15 August 2020; Revised: 29 January 2021; Accepted: 12 February 2021; Published: April 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.585

Subjects:
Primary: 16D70 , 16S90 , 20E06

Keywords: cancellation , generalized torsion module , stable module

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 2 • April 2021
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