Bases for existence varieties of strict regular semigroups

Existence varieties (or e-varieties) were introduced by Hall as classes of regular semigroups closed for direct products, homomorphic images and regul ar subsemigroups. They can be characterized by thc identities satisfied by all regular unary semigroups (S,'), that is a --> a' is an inverse unary op eration on S, where S is in the given e-variety. In this way, we may speak of a basis of (identities of) an e-variety. We provide several bases for a number of sub-e-varieties of the e-variety S R of strict semigroups. The latter are best characterized as subdirect prod ucts of completely (0-) simple semigroups. These sub-e-varieties of SR incl ude those of all of whose members are: completely regular, E-solid, orthodo x, inverse, overabelian, combinatorial and semigroups whose core is either overabelian or combinatorial. These e-varieties are depicted in two diagram s.