2022/09/28 by Michael Kinyon, Kinyon, Michael, David Stanovský +1 · 1 citation
Computer Science · Decision Sciences · #08A30 #20F19 #20M18 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2209.13805
openalex publication_date 2022/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to conjugation in inverse semigroups. Subsequently we prove that solvable and nilpotent inverse semigroups are groups.