2023/09/06 by James Renshaw, Renshaw, James, William Warhurst +1
Computer Science · Decision Sciences · Mathematics · #20M10 #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2309.02831
openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1995 Grillet defined the concept of a stratified semigroup and a stratified semigroup with zero. The present authors extended that idea to include semigroups with a more general base and proved, amongst other things, that finite semigroups in which the H-classes contain idempotents, are semilattices of stratified extensions of completely simple semigroups, and every strict stratified extension of a Clifford semigroup is a semilattice of stratified extensions of groups. We continue this work here by considering the multiplicative semigroup of Dedekind domains and show in particular that quotients of such rings have a multiplicative structure that is a (finite) Boolean algebra of stratified extensions of groups.