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arXiv · 2507.22182

Skew braces, near-rings, skew rings, dirings

Alberto Facchini
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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.

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Alberto Facchini. 2025-07-29. Skew braces, near-rings, skew rings, dirings. https://doi.org/10.46298/cm.16621

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