< Back to previous page

Publication

The algebraic structure of left semi-trusses

Journal Contribution - Journal Article

The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative “distributive” laws were defined. In an effort to study these “left distributive” laws and the interaction they entail on the algebraic structures, Brzeziński introduced skew left trusses and left semi-trusses. In particular the class of left semi-trusses is very wide, since it contains all rings, associative algebras and distributive lattices. In this paper, we investigate the subclass of left semi-trusses that behave like the algebraic structures that came up in the study of the Yang-Baxter equation. We study the interaction of the operations and what this interaction entails on their respective semigroups. In particular, we prove that in the finite case the additive structure is a completely regular semigroup. Secondly, we apply our results on a particular instance of a left semi-truss called an almost left semi-brace, introduced by Miccoli to study its algebraic structure. In particular, we show that one can associate a left semi-brace to any almost left semi-brace. Furthermore, we show that the set-theoretic solutions of the Yang-Baxter equation originating from almost left semi-braces arise from this correspondence.

Journal: J. Pure Appl. Algebra
ISSN: 0022-4049
Issue: 2
Volume: 225
Publication year:2021
Keywords:Distributive law, Quantum Yang-Baxter equation, Semi-brace, Semi-truss, Set-theoretic solution
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:1
Authors:Regional
Authors from:Higher Education
Accessibility:Closed