On R-unipotent semigroups with ΠL¹-embeddable band of idempotents

Abstract

© 2015, Springer Science+Business Media New York. Let ΠL1denote a direct power of L1, the two-element left zero semigroup with identity adjoined. We prove that the semigroups in the title are embeddable into transformation semigroups which naturally generalize the Vagner one-point completion of the symmetric inverse semigroup. We give some examples and show that our representation provides a convenient way to construct E-unitary covers and embeddings of E-unitary such semigroups into semidirect products of ΠL1-embeddable bands by groups.