A. Facchini

collaborators

10 papers

math.GR2026

Digroups, their canonical pretorsion theory, and diheaps

Alberto Facchini, Carmelo Antonio Finocchiaro

In the category of digroups there is a natural pretorsion theory in which the torsion-free digroups are all groups, and torsion digroups form a category isomorphic to the category…

math.GR2026

Right groups, left quasigroups, and right heaps

Andrea Albano, Alberto Facchini, Marzia Mazzotta +1

A right group is a semigroup $(S, \cdot)$ in which, for every $a, b \in S$ , there is a unique $x \in S$ such that $a \cdot x = b$ . In this article, we develop the theory of heaps starting…

math.GR2026

Right groups and the set-theoretic Yang-Baxter equation

Andrea Albano, Alberto Facchini, Marzia Mazzotta +1

In this paper, we provide techniques to obtain left non-degenerate set-theoretic solutions of the Yang-Baxter equation, drawing on the class of right groups. To this end, we introd…

math.CT2026

A pretorsion theory for right groups

Alberto Facchini, Carmelo Antonio Finocchiaro

Let $S$ be a right group. Then there exist two congruences $\sim$ and $\equiv$ on $S$ such that $S$ is the product of its quotient semigroups $S / \sim$ and $S / \equiv$ , where $S/…

math.RA2025

Skew braces, near-rings, skew rings, dirings

Alberto Facchini

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 i…

math.RA2025

Trusses, ditrusses, weak trusses

Alberto Facchini

In this paper we extend to left skew trusses $(T, +, \circ, I ¨ )$ previous work on left skew rings. We had presented a left skew ring as a group $(N, +)$ with two binary operations $\ci…