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Cancellation and stability properties of generalized torsion modules

Johnson, FEA; (2021) Cancellation and stability properties of generalized torsion modules. Rocky Mountain Journal of Mathematics , 51 (2) pp. 585-591. 10.1216/rmj.2021.51.585. Green open access

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Abstract

Given a module X over a ring Λ its stability class consists of all modules X ′ such that X ⊕ Λ a ≅ X ′ ⊕ Λ b 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.

Type: Article
Title: Cancellation and stability properties of generalized torsion modules
Open access status: An open access version is available from UCL Discovery
DOI: 10.1216/rmj.2021.51.585
Publisher version: http://doi.org/10.1216/rmj.2021.51.585
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Cancellation, generalized torsion module, stable module
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10125437
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