A. Facchini

activity

20052026

most citedFactorizations of polynomials with integral non-negative coefficients

21 citations · 56 across the 28 of their papers we have counts for

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22 papers · 1 filter

math.RA2025

Trusses, ditrusses, weak trusses

Alberto Facchini

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

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★ 2 cited

Homomorphisms with semilocal endomorphism rings between modules

Federico Campanini, Susan F. El-Deken, Alberto Facchini

We study the category $Morph (Mod R)$ whose objects are all morphisms between two right $R$ -modules. The behavior of objects of $\operatorname{Morph}(\…

math.RA2025★ 5 cited

On a category of extensions whose endomorphism rings have at most four maximal ideals

Federico Campanini, Alberto Facchini

We describe the endomorphism ring of a short exact sequences $0 \to A_{R} \to B_{R} \to C_{R} \to 0$ with $A_{R}$ and $C_{R}$ uniserial modules and the behavior of these short exact sequence…

math.RA2025

Exactness of cochain complexes via additive functors

Federico Campanini, Alberto Facchini

We investigate the relation between the notion of $e$ -exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor $P\colon\op…

math.RA2023

Semidirect products in Universal Algebra

Alberto Facchini, David Stanovský

First of all, we recall the well known notion of semidirect product both for classical algebraic structures (like groups and rings) and for more recent ones (digroups, left skew br…