Semigroup Forum

, Volume 88, Issue 3, pp 647–669 | Cite as

Classes of semigroups modulo Green’s relation \(\mathcal{H}\)

RESEARCH ARTICLE

Abstract

Inverse semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green’s relation \(\mathcal{H}\), or in terms of the set of completely regular elements H(S). Results are obtained both for the regular and the non-regular cases. We then study the interplays between these new classes of semigroups, as well as with various known classes notably of inverse, orthodox, E-solid and cryptic semigroups.

Keywords

Generalized inverses Green’s relations Semigroups 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Université Paris-Ouest Nanterre-La Défense, Laboratoire Modal’XParisFrance

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