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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

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
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa53070
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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. 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.
Keywords: Truss; heap; ring; brace; module
College: College of Science
Start Page: 2050010