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Trusses: Paragons, ideals and modules

Tomasz Brzezinski Orcid Logo

Journal of Pure and Applied Algebra, Volume: 224, Issue: 6, Start page: 106258

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.1016/j.jpaa.2019.106258

Abstract

Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions of ideals and paragons in trusses are introduced and several constructions of trusses are presented. A full classificatio...

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Published in: Journal of Pure and Applied Algebra
ISSN: 0022-4049
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa52083
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first_indexed 2019-09-25T14:19:24Z
last_indexed 2023-03-14T04:05:45Z
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spelling 2023-03-13T12:04:42.2153284 v2 52083 2019-09-25 Trusses: Paragons, ideals and modules 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2019-09-25 SMA Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions of ideals and paragons in trusses are introduced and several constructions of trusses are presented. A full classification of truss structures on the Abelian group of integers is given. Modules over trusses are defined and their basic properties and examples are analysed. In particular, the sufficient and necessary condition for a sub-heap of a module to induce a module structure on the quotient heap is established. Journal Article Journal of Pure and Applied Algebra 224 6 106258 Elsevier BV 0022-4049 Truss, Heap, Ideal, Paragon, Module 1 6 2020 2020-06-01 10.1016/j.jpaa.2019.106258 http://dx.doi.org/10.1016/j.jpaa.2019.106258 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-03-13T12:04:42.2153284 2019-09-25T09:34:42.0501627 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1
title Trusses: Paragons, ideals and modules
spellingShingle Trusses: Paragons, ideals and modules
Tomasz Brzezinski
title_short Trusses: Paragons, ideals and modules
title_full Trusses: Paragons, ideals and modules
title_fullStr Trusses: Paragons, ideals and modules
title_full_unstemmed Trusses: Paragons, ideals and modules
title_sort Trusses: Paragons, ideals and modules
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzezinski
format Journal article
container_title Journal of Pure and Applied Algebra
container_volume 224
container_issue 6
container_start_page 106258
publishDate 2020
institution Swansea University
issn 0022-4049
doi_str_mv 10.1016/j.jpaa.2019.106258
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1016/j.jpaa.2019.106258
document_store_str 0
active_str 0
description Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions of ideals and paragons in trusses are introduced and several constructions of trusses are presented. A full classification of truss structures on the Abelian group of integers is given. Modules over trusses are defined and their basic properties and examples are analysed. In particular, the sufficient and necessary condition for a sub-heap of a module to induce a module structure on the quotient heap is established.
published_date 2020-06-01T04:04:15Z
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score 11.035634

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