Implications for semigroups embeddable in orthocryptogroups (Q1097970)

A semigroup which is a union of groups is called completely regular. A completely regular semigroup whose idempotents form a subsemigroup is called an orthogroup. An orthogroup is called an orthocryptogroup if its group components are congruence classes. The class of semigroups embeddable in orthocryptogroups obviously forms a quasivariety of semigroups. This paper contains a system of quasi-identities \([=universal\) Horn formulas] which describe the above quasivariety. The system is essentially infinite because, as it follows from Mal'tsev's result, the quasivariety of semigroups embeddable in groups cannot be described by a finite system of quasi-identities. Let V be a variety of idempotent semigroups. Orthocryptogroups whose subsemigroups of idempotents belong to V are called V-orthocryptogroups. Quasi-identities characterizing semigroups embeddable in V- orthocryptogroups for any given V are found.