Minimal Noncryptic e-Varieties of Regular Semigroups Original Research Article

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 corollaries, we prove that an e-variety of regular semigroups is cryptic if and only if its intersections with the variety of all completely regular semigroups and the variety of all inverse semigroups are cryptic. We also find an equational characterization of group-bound cryptic varieties; this generalises some recent results by Doyle and Yeh.