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The Baer–Kaplansky Theorem for all abelian groups and modules

Simion Breaz Orcid Logo, Tomasz Brzezinski Orcid Logo

Bulletin of Mathematical Sciences, Volume: 12, Issue: 01, Pages: 1 - 12

Swansea University Author: Tomasz Brzezinski Orcid Logo

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Abstract

It is shown that the Baer-Kaplansky theorem can be extended to all abelian groups provided that the rings of endomorphisms of groups are replaced by trusses of endomorphisms of corresponding heaps. That is, every abelian group is determined up to isomorphism by its endomorphism truss and every isomo...

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Published in: Bulletin of Mathematical Sciences
ISSN: 1664-3607 1664-3615
Published: World Scientific Pub Co Pte Ltd 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56478
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Abstract: It is shown that the Baer-Kaplansky theorem can be extended to all abelian groups provided that the rings of endomorphisms of groups are replaced by trusses of endomorphisms of corresponding heaps. That is, every abelian group is determined up to isomorphism by its endomorphism truss and every isomorphism between two endomorphism trusses associated to some abelian groups $G$ and $H$ is induced by an isomorphism between $G$ and $H$ and an element from $H$. This correspondence is then extended to all modules over a ring by considering heaps of modules. It is proved that the truss of endomorphisms of a heap associated to a module $M$ determines $M$ as a module over its endomorphism ring.
Keywords: Abelian group; heap; endomorphism truss
College: College of Science
Issue: 01
Start Page: 1
End Page: 12