A. Facchini

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5 papers · 1 filter

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…

math.RA2025

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

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…