From pre-trusses to skew braces
Brzeziński, Tomasz (Swansea University. Department of Mathematics)
Mereta, Stefano (Swansea University. Department of Mathematics)
Rybołowicz, Bernard (Heriot-Watt University. Department of Mathematics)

Date:	2022
Abstract:	An algebraic system consisting of a set together with an associative binary and a ternary heap operations is studied. Such a system is termed a pre-truss and if a binary operation distributes over the heap operation on one side we call it a near-truss. If the binary operation in a near-truss is a group operation, then it can be specified or retracted to a skew brace, the notion introduced in [8]. On the other hand if the binary operation in a near-truss has identity, then it gives rise to a skewring as introduced in [14]. Congruences in pre- and near-trusses are shown to arise from normal sub-heaps with an additional closure property of equivalence classes that involves both the ternary and binary operations. Such sub-heaps are called paragons. A necessary and sufficient criterion on paragons under which the quotient of a unital near-truss corresponds to a skew brace is derived. Regular elements in a pre-truss are defined as elements with left and right cancellation properties; following the ringtheoretic terminology, pre-trusses in which all non-absorbing elements are regular are termed domains. The latter are described as quotients by completely prime paragons, also defined hereby. Regular pre-trusses and near-trusses as domains that satisfy the Ore condition are introduced and pre-trusses of fractions are constructed through localisation. In particular, it is shown that near-trusses of fractions without an absorber correspond to skew braces.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Pre-truss ; Near-truss ; Heap ; Skew brace ; Near-ring
Published in:	Publicacions matemàtiques, Vol. 66 Núm. 2 (2022) , p. 683-714 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/402240
DOI: 10.5565/PUBLMAT6622206

32 p, 370.4 KB

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