2023
DOI: 10.1007/s00233-023-10394-7
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On the structure of semigroups whose regular elements are completely regular

Xavier Mary

Abstract: In this article, we study the structure of strongly 2-chained semigroups, which can be defined alternatively as semigroups whose regular elements are completely regular. The main result is a semilattice decomposition of these semigroups in terms of ideal extensions of completely simple semigroups by poor semigroups and idempotent-free semigroups.

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