ACTA issues

## $E$-solid locally inverse semigroups

Tamás Dékány, Mária B. Szendrei, István Szittyai

Acta Sci. Math. (Szeged) 85:3-4(2019), 381-411
61/2018

 Abstract. We prove that if $S$ is an $E$-solid locally inverse semigroup, and $\rho$ is an inverse semigroup congruence on $S$ such that the idempotent classes of $\rho$ are completely simple semigroups then $S$ is embeddable into a $\lambda$-semidirect product of a completely simple semigroup by $S/\rho$. Consequently, the $E$-solid locally inverse semigroups turn out to be, up to isomorphism, the regular subsemigroups of $\lambda$-semidirect products of completely simple semigroups by inverse semigroups. DOI: 10.14232/actasm-018-311-5 AMS Subject Classification (1991): 20M10, 20M17 Keyword(s): regular semigroups, E-solid locally inverse semigroups, $\lambda$-semidirect product, extensions Received July 3, 2018. (Registered under 61/2018.)