4 papers
Set-theoretic solutions of the Pentagon Equation
Ilaria Colazzo, Eric Jespers, Lukasz Kubat
A set-theoretic solution of the Pentagon Equation on a non-empty set is a map such that , where $s_{12}=s\times\mathrm{id}…
The algebraic structure of left semi-trusses
Ilaria Colazzo, Arne Van Antwerpen
The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative "…
The matched product of set-theoretical solutions associated with shelves
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
We investigate the matched product of solutions associated with right and left shelves. First, we prove that the requirements to provide the matched product of solutions that come…
The matched product of the solutions to the Yang-Baxter equation of finite order
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
In this work, we focus on the set-theoretical solutions of the Yang-Baxter equation which are of finite order and not necessarily bijective. We use the matched product of solutions…