Abstract

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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.