2010/03/22 by Jehan A. Al-bar, Jehan Al-Bar, Al-Bar, Jehan +2
Computer Science · Mathematics · #20M10 #Advanced Algebra and Logic #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20M10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1003.4136
arxiv created 2010/03/22 · openalex publication_date 2010/03/22 · arxiv updated 2010/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of an adequate transversal of an abundant semigroup was introduced by El-Qallali in [8] whilst in [7], he and Fountain initiated the study of quasi-adequate semigroups as natural generalisations of orthodox semigroups. In this work we provide a structure theorem for adequate transversals of certain types of quasi-adequate semigroup and from this deduce Saito's classic result on the structure of inverse transversals of orthodox semigroups. We also apply it to left ample adequate transversals of left adequate semigroups and provide a structure for these based on semidirect products of adequate semigroups by left regular bands.