MINIMAL NONCRYPTIC E-VARIETIES OF REGULAR-SEMIGROUPS

We describe all minimal noncryptic e-varieties of regular semigroups, thus generalising earlier results by Rasin and Reilly that dealt with the completely regular and the inverse cases, respectively. As corolla ries, we prove that an e-variety of regular semigroups is cryptic if a nd only if its intersections with the variety of all completely regula r semigroups and the variety of all inverse semigroups are cryptic. We also find an equational characterization of group-bound cryptic varie ties; this generalises some recent results by Doyle and Yeh. (C) 1996 Academic Press, Inc.