Semigroup Forum

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

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

  • Xavier MaryEmail author
Research Article


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.


Extended Green’s relations Abundant semigroups Restriction semigroups Generalized inverses 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Université Paris NanterreNanterreFrance

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