Semigroup Forum

, Volume 94, Issue 3, pp 738–776 | Cite as

On \((E,\widetilde{\mathcal {H}}_E)\)-abundant semigroups and their subclasses

Research Article

Abstract

We study semigroups that behave nicely with respect to a distinguished subset of idempotents E, both in terms of the extended Green’s relations \(\widetilde{\mathcal {K}}_E\) and as unary semigroups. New structure theorems are given, notably in the case of central idempotents. Finally, the decomposition theorems are applied to the study of regular semigroups with particular generalized inverses.

Keywords

Extended Green’s relations Abundant semigroups Restriction semigroups Generalized inverses 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Université Paris NanterreNanterreFrance

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