$E$-solid locally inverse semigroups
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.
math.GR↗