Associative Pentagon Algebras
Marzia Mazzotta, Agata Pilitowska

TL;DR
This paper studies a special class of algebraic structures called associative pentagon algebras, characterizing their properties and providing constructions and examples based on semigroup theory.
Contribution
It introduces and fully characterizes associative pentagon algebras where both operations form semigroups, expanding understanding of solutions to the Pentagon Equation.
Findings
Two families of associative pentagon algebras described
Complete characterization via semigroup equations
Constructed examples and classes provided
Abstract
A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra such that is a semigroup and the operations and are related by two additional equations. This paper aims to investigate associative pentagon algebras in which is also a semigroup. We introduce and describe two families of associative pentagon algebras which are strongly determined by the properties of the semigroup . We present a complete characterization of such algebras using semigroup equations. We also provide constructions of such associative pentagon algebras and give several classes of examples.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms
