On Existence Varieties of E-solid Semigroups

E

-solid semigroups, a theory of e-varieties including appropriate notions of biidentities and biinvariant congruences is presented, such that, together with bifree objects, these notions inherit the properties and interrelations well known from universial algebra. This theory generalizes the previously developed such theory for orthodox semigroups.

As an application, the bifree objects in certain e-varieties of E-solid locally orthodox semigroups, which are constructed by means of Malcev products from a varities of bands, groups and completely simple semigroups, are described as subsemigroups in suitable Pastijn products of some bands by relatively bifree completely simple semigroups. As a consequence, it follows that every regular E-solid locally orthodox semigroup regularly divides a so-called solid Pastijn product of a band by a completely simple semigroup.