Regular semigroups: amalgamation and the lattice of existence varieties

A class of regular semigroups is called an existence variety (ore-variety) if it is closed under , and , the operations of taking all morphic images, all regular subsemigroups, and all direct products, respectively; and such classes were previously shown (like varieties) to be determined by sets of identities. We determine whiche-varieties of regular semigroups have the amalgamation property. Preliminary results include (1) a construction of the lattice ofe-varieties of generalized inverse semigroups and (2) the result that thee-variety of combinatorial, strict, regular semigroups is the leaste-variety which is notE-solid.Dedicated to Professor G. B. Preston, on the occasion of his 65th birthdayPresented by Ralph Freese.