Work

Associative pentagon algebras

Year: 2026

Type: article

Abstract: A set-theoretic solution to the Pentagon Equation can be described as a pentagon algebra $$(S, \cdot , *)$$ ( S , · , ∗ ) such that $$(S, \cdot )$$ ( S , · ) is a semigroup and the operations $$\cdot $$ · and $$*$$ ∗ are related by two additional equations. This paper aims to investigate associative pentagon algebras in which $$(S, *)$$ ( S , ∗ ) is also a semigroup. We introduce and describe two families of associative pentagon algebras which are strongly determined by the properties of the semigroup $$(S,*)$$ ( S , ∗ ) . 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.

Source: Semigroup Forum

DOI: 10.1007/s00233-026-10646-2

Authors: Marzia Mazzotta, Agata Pilitowska

Institutions: University of Salento, Warsaw University of Technology

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politechnika Warszawska, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni