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

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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.

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  1. Université Paris Nanterre, Laboratoire Modal’X 200 Avenue de la République, 92000, Nanterre, France

    Xavier Mary

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  1. Xavier Mary
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Correspondence to Xavier Mary.

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Communicated by Victoria Gould.

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Mary, X. On \((E,\widetilde{\mathcal {H}}_E)\)-abundant semigroups and their subclasses. Semigroup Forum 94, 738–776 (2017). https://doi.org/10.1007/s00233-017-9856-7

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