Hyperbolicity of Semigroup Algebras II
E. Iwaki, E. Jespers, S. O. Juriaans, A. C. Souza Filho

TL;DR
This paper completes the classification of finite semigroups whose rational semigroup algebra has a hyperbolic unit group, focusing on the case where the semigroup is semi-simple, building on prior classifications of units in semigroup rings.
Contribution
It provides a complete classification of semi-simple finite semigroups with hyperbolic unit groups in their rational semigroup algebras, extending previous partial results.
Findings
Classification of semi-simple finite semigroups with hyperbolic unit groups
Extension of prior classifications of units in semigroup rings
Identification of algebraic structures leading to hyperbolic unit groups
Abstract
In 1996 Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra %over a field of characteristic zero, contains a -order with hyperbolic unit group. In this paper we complete this classification by handling the case in which the semigroup is semi-simple.
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Taxonomy
Topicssemigroups and automata theory · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory
