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The Baer–Kaplansky Theorem for all abelian groups and modules
Bulletin of Mathematical Sciences, Volume: 12, Issue: 01, Pages: 1 - 12
Swansea University Author:
Tomasz Brzezinski
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DOI (Published version): 10.1142/s1664360721500053
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...
Published in: | Bulletin of Mathematical Sciences |
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ISSN: | 1664-3607 1664-3615 |
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World Scientific Pub Co Pte Ltd
2021
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URI: | https://cronfa.swan.ac.uk/Record/cronfa56478 |
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2022-04-08T12:22:33.9913900 v2 56478 2021-03-22 The Baer–Kaplansky Theorem for all abelian groups and modules 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2021-03-22 SMA 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. Journal Article Bulletin of Mathematical Sciences 12 01 1 12 World Scientific Pub Co Pte Ltd 1664-3607 1664-3615 Abelian group; heap; endomorphism truss 13 4 2021 2021-04-13 10.1142/s1664360721500053 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2022-04-08T12:22:33.9913900 2021-03-22T09:19:01.1258882 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Simion Breaz 0000-0002-8506-4526 1 Tomasz Brzezinski 0000-0001-6270-3439 2 56478__19683__6b14e588c7d94a518a411f7685e36a36.pdf 56478.pdf 2021-04-19T13:27:47.1372582 Output 289169 application/pdf Version of Record true © The Author(s). It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License true eng https://creativecommons.org/licenses/by/4.0 |
title |
The Baer–Kaplansky Theorem for all abelian groups and modules |
spellingShingle |
The Baer–Kaplansky Theorem for all abelian groups and modules Tomasz Brzezinski |
title_short |
The Baer–Kaplansky Theorem for all abelian groups and modules |
title_full |
The Baer–Kaplansky Theorem for all abelian groups and modules |
title_fullStr |
The Baer–Kaplansky Theorem for all abelian groups and modules |
title_full_unstemmed |
The Baer–Kaplansky Theorem for all abelian groups and modules |
title_sort |
The Baer–Kaplansky Theorem for all abelian groups and modules |
author_id_str_mv |
30466d840b59627325596fbbb2c82754 |
author_id_fullname_str_mv |
30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski |
author |
Tomasz Brzezinski |
author2 |
Simion Breaz Tomasz Brzezinski |
format |
Journal article |
container_title |
Bulletin of Mathematical Sciences |
container_volume |
12 |
container_issue |
01 |
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1 |
publishDate |
2021 |
institution |
Swansea University |
issn |
1664-3607 1664-3615 |
doi_str_mv |
10.1142/s1664360721500053 |
publisher |
World Scientific Pub Co Pte Ltd |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
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description |
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. |
published_date |
2021-04-13T04:11:28Z |
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1763753788513976320 |
score |
11.021648 |