E-solid locally inverse semigroups

2018/07/03 by Dékány, Tamás, Szendrei, Mária B., Szittyai, István
#20M10 #20M17 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1807.01265

Abstract

We prove that if S is an E-solid locally inverse semigroup, and ρ is an inverse semigroup congruence on S such that the idempotent classes of ρ are completely simple semigroups then S is embeddable into a λ-semidirect product of a completely simple semigroup by S/ρ. Consequently, the E-solid locally inverse semigroups turn out to be, up to isomorphism, the regular subsemigroups of λ-semidirect products of completely simple semigroups by inverse semigroups.

Related

• E-disjunctive inverse semigroups
• Partial actions and an embedding theorem for inverse semigroups
• Cross-connection structure of locally inverse semigroups
• Classes of semigroups modulo Green's relation H
• Normal extensions and full restricted semidirect products of inverse semigroups