On the structure of regular H-cryptogroups

Abstract

We introduce the concepts of Green-relations on H-abundant semigroups. By using the generalized strong semilattice of semigroups, we show that an H-cryptogroup is a regular H-cryptogroup if and only if it is an HG-strong semilattice of completely J-simple semigroups. This result not only extends a known result of Petrich from the class of completely regular semigroups to the class of semi abundant semi groups but also generalizes a well known result of Fountainon superabundant semigroups from the class of abundant semigroups to the class of semiabundant semigroups.