ON EXISTENCE VARIETIES OF E-SOLID OR LOCALLY INVERSE-SEMIGROUPS AND E-INVARIANT CONGRUENCES

An existence variety (or e-variety) of regular semigroups is a class o f regular semigroups which is closed under P, S(e), and H. This concep t was introduced by T. E. Hall and independently for orthodox semigrou ps by J. Kadourek and M. B. Szendrei who called them bivarieties. In t his paper we show some properties of e-varieties of E-solid regular se migroups when they are also completely semisimple, combinatorial, or c ryptic. Also the existence of e-free objects in e-varieties of E-solid (or locally inverse) regular semigroups enables us to, analogously to the case for varieties of inverse semigroups, determine an order-inve rting one-to-one correspondence between e-invariant congruences and e- varieties of E-solid (or locally inverse) regular semigroups. (C) 1994 Academic Press, Inc.