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We use Malcev product of semigroups satisfying some axiomatic conditions to describe the structure of superabundant semigroups and some of its subclasses. Some characterization theorems of these kinds of semigroups are given. [ABSTRACT FROM AUTHOR]

In this paper, we study the structure of a superabundant semigroup S whose set of idempotents E(S) forms a subsemigroup. We call such a semigroup a cyber-group because it is a generalization of orthogroups in the class of completely regular semigroups studied by Petrich and Reilly. We show that a cyber-group can be expressed as a semilattice of rectangular monoids. Thus, our result generalizes the well-known result obtained by Petrich in 1987 for orthogroups. Some properties of cyber-groups are given and some special superabundant semigroups are discussed. [ABSTRACT FROM AUTHOR]