Skew braces, near-rings, skew rings, dirings
Rings and Algebras
2026-03-18 v3
Abstract
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring by two operations, one associative and the other left distributive. Two algebraic structures naturally appear: left skew rings and left weak rings, whose categories turn out to be canonically isomorphic.
Cite
@article{arxiv.2507.22182,
title = {Skew braces, near-rings, skew rings, dirings},
author = {Alberto Facchini},
journal= {arXiv preprint arXiv:2507.22182},
year = {2026}
}