Salvatore Tringali

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20242026

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6 papers · 1 filter

math.RA2026

Power monoids and their arithmetic: a survey

Salvatore Tringali

The non-empty finite subsets of a multiplicatively written monoid form a monoid under setwise multiplication. The same holds for finite subsets containing the identity element. Par…

math.RA2025

On global isomorphisms and a closure property of semigroups

Lingxi Li, Salvatore Tringali

Let $S$ be a semigroup (written multiplicatively). Endowed with the operation of setwise multiplication induced by $S$ on its parts, the non-empty subsets of $S$ form themselves a…

math.RA2025

On the arithmetic of power monoids

Laura Cossu, Salvatore Tringali

Given a monoid $H$ (written multiplicatively), the family $P_{fin, 1} (H)$ of all non-empty finite subsets of $H$ containing the identity element $1_{H}$ is itself a…

math.RA2025

The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties

Federico Campanini, Laura Cossu, Salvatore Tringali

We introduce and investigate the category $AtoMon$ of atomic monoids and atom-preserving monoid homomorphisms, which is a (non-full) subcategory of the usual category of m…

math.RA2024

Semigroups of ideals and isomorphism problems

Pedro A. Garcia-Sanchez, Salvatore Tringali

Let $H$ be a monoid (written multiplicatively). We call $H$ Archimedean if, for all $a, b \in H$ such that $b$ is a non-unit, there is an integer $k \geq 1$ with $b^{k} \in H a H$ ; stro…

math.RA2024

On the isomorphism problem for power semigroups

Salvatore Tringali

Let $P (S)$ be the semigroup obtained by equipping the family of all non-empty subsets of a (multiplicatively written) semigroup $S$ with the operation of setwise multiplic…