'Institute of Geophysics of the National Academy of Sciences of Ukraine by S.I. Subbotin name'
Abstract
A semigroup S is called F−semigroup if there exists a group congruence ρ on S such that every ρ −class contains a greatest element with respect to the natural partial order ≤ of S . This generalizes the concept of F−inverse semigroups introduced by V. Wagner
in 1961 and investigated by McFadden and O’Caroll in 1971. Five different characterisations of general F−semigroups S are given: by means of residuals, by special principal anticones, by properties of the set of idempotents, by the maximal elements in (S, ≤) and finally, an axiomatic one using an additional unary operation. Also, F−semigroups in special classes are considered; in particular, inflations of semigroups and strong semi-
lattices of monoids are studied.Centro de Matemática da Universidade do MinhoFundação para a Ciência e a Tecnologia (FCT
