Resumen de Semigroups of cosets of semigroups: variations on a Dubreil theme

Boris M. Schein

• In his seminal article of 1941, Paul Dubreil introduced \textit{complexes forts} of semigroups. Strong subsets of a semigroup $S$ form another semigroup under a natural multiplication. Properties of this semigroup are studied and some open problems raised (specially when $S$ is a group or an inverse semigroup). Also, a simple proof of a known result is given: every inverse semigroup can be isomorphically embedded in the semigroup of cosets of a group.