Associative pentagon algebras
Abstract
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.
Fields of Study & Subjects
Advanced Topics in Algebra
Matrix Theory and Algorithms
Publication details
- Journal / source
- Semigroup Forum
- Volume
- 113
- Issue
- 1
- Pages
- 202–232
- Publication date
- 16 June 2026
- Language
- EN