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Congruence classes and extensions of rings with an application to braces

Tomasz Brzezinski Orcid Logo, Bernard Rybolowicz

Communications in Contemporary Mathematics, Start page: 2050010

Swansea University Authors: Tomasz Brzezinski Orcid Logo, Bernard Rybolowicz

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DOI (Published version): 10.1142/s0219199720500108

Abstract

Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring R by an ideal I is a paragon in the truss T()T(R) associated to R. S...

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Published in: Communications in Contemporary Mathematics
ISSN: 0219-1997 1793-6683
Published: World Scientific Pub Co Pte Lt 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53070
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first_indexed 2019-12-23T19:48:35Z
last_indexed 2021-09-09T03:13:41Z
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spelling 2021-09-08T14:50:33.9702422 v2 53070 2019-12-23 Congruence classes and extensions of rings with an application to braces 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false c821b8f926d58c3b7955b533a5c1472b Bernard Rybolowicz Bernard Rybolowicz true false 2019-12-23 SMA Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring R by an ideal I is a paragon in the truss T()T(R) associated to R. Second, an extension of a truss by a one-sided module is described. Even if the extended truss is associated to a ring, the resulting object is a truss, never a ring, unless the module is trivial. On the other hand, if the extended truss is associated to a brace, the resulting truss is also associated to a brace, irrespective of the module used. Journal Article Communications in Contemporary Mathematics 2050010 World Scientific Pub Co Pte Lt 0219-1997 1793-6683 Truss; heap; ring; brace; module 25 2 2020 2020-02-25 10.1142/s0219199720500108 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2021-09-08T14:50:33.9702422 2019-12-23T12:35:57.9383051 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1 Bernard Rybolowicz 2 53070__16161__e0a9e8b5773c4276b3248ddab1989986.pdf truss_ext_rev.pdf 2019-12-23T12:44:56.1034615 Output 367228 application/pdf Accepted Manuscript true 2021-02-25T00:00:00.0000000 true eng
title Congruence classes and extensions of rings with an application to braces
spellingShingle Congruence classes and extensions of rings with an application to braces
Tomasz Brzezinski
Bernard Rybolowicz
title_short Congruence classes and extensions of rings with an application to braces
title_full Congruence classes and extensions of rings with an application to braces
title_fullStr Congruence classes and extensions of rings with an application to braces
title_full_unstemmed Congruence classes and extensions of rings with an application to braces
title_sort Congruence classes and extensions of rings with an application to braces
author_id_str_mv 30466d840b59627325596fbbb2c82754
c821b8f926d58c3b7955b533a5c1472b
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
c821b8f926d58c3b7955b533a5c1472b_***_Bernard Rybolowicz
author Tomasz Brzezinski
Bernard Rybolowicz
author2 Tomasz Brzezinski
Bernard Rybolowicz
format Journal article
container_title Communications in Contemporary Mathematics
container_start_page 2050010
publishDate 2020
institution Swansea University
issn 0219-1997
1793-6683
doi_str_mv 10.1142/s0219199720500108
publisher World Scientific Pub Co Pte Lt
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
document_store_str 1
active_str 0
description Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring R by an ideal I is a paragon in the truss T()T(R) associated to R. Second, an extension of a truss by a one-sided module is described. Even if the extended truss is associated to a ring, the resulting object is a truss, never a ring, unless the module is trivial. On the other hand, if the extended truss is associated to a brace, the resulting truss is also associated to a brace, irrespective of the module used.
published_date 2020-02-25T04:05:51Z
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score 11.035634

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