On the structure of semigroups whose regular elements are completely regular. (English) Zbl 1530.20181
Summary: 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.
Keywords:
chains of idempotents; completely regular elements; ideal extensions; semilattice decompositionsReferences:
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