2015/10/18 by Attila Nagy, Nagy, Attila
Computer Science · Mathematics · #20M10 #20M30 #Advanced Algebra and Logic #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20M10 #msc:20M30 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1510.05291
arxiv created 2015/10/18 · openalex publication_date 2015/10/18 · arxiv updated 2015/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a semigroup, Λ a non-empty set and P a mapping of Λ into S. The set S× Λ together with the operation ∘ P defined by (s, λ)∘ P(t, μ)=(sP(λ)t, μ) form a semigroup which is denoted by (S, Λ, ∘ P). Using this construction, we prove a common connection between the semigroups S, S/θ and S/θ^*=(S/θ)/(θ^*/θ), where θ and θ^*/θ are the kernels of the right regular representations of S and S/θ, respectively. We also prove an embedding theorem for the semigroup (S, S/θ, ∘ p), where S is a left equalizer simple semigroup without idempotents, and P maps every θ-class of S into itself.