Some orthodox monoids with associate inverse subsemigroups

By an associate inverse subsemigroup of a regular semigroup $S$ we mean a subsemigroup $T$ of $S$ containing a least associate of each $x \in S$, in relation to the natural partial order $\leq_S$ in $S$. In this paper we investigate a class of orthodox monoids with an associate inverse subsemigroup and obtain a known description of uniquely unit regular orthodox semigroups as a corollary. Also, by considering a more general situation, we identify the homomorphic image of a kind of semidirect product of a band with identity by an inverse monoid, thus extending a known result for unit regular orthodox semigroups.Portuguese Foundation for Science and Technology (FCT) through the Research Centre CMA

Associate inverse subsemigroups of regular semigroups

By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x ∈ S, in relation to the natural partial order ≤S. We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions. As a articular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity element.Fundação para a Ciência e a Tecnologia (FCT

A note on dual prehomomorphisms from a group into the Margolis–Meakin expansion of a group

The original article has been updated. Open Access funding enabled and organized by Projekt DEAL.Gefördert im Rahmen des Projekts DEA