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The product of the idempotents and an \(\mathcal{H}\)-class of the finite full transformation semigroup

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Abstract

We investigate the set products S=EH, where E is the set of idempotents of a finite full transformation semigroup T X and H is an arbitrary \(\mathcal{H}\)-class of T X . We show that S is a semigroup and is a union of \(\mathcal{H}\)-classes of T X . We determine the nature of this union through use of Hall’s Marriage Lemma. We describe Green’s relations and thereby show that S has regular elements of all possible ranks and that \(\operatorname{Reg}(S)\) forms a right ideal of S.

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Authors and Affiliations

  1. Dept. of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, Essex, UK

    Peter M. Higgins

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  1. Peter M. Higgins
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Correspondence to Peter M. Higgins.

Additional information

Communicated by Jean-Eric Pin.

Dedicated to the memory of John Mackintosh Howie (1936–2011).

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Higgins, P.M. The product of the idempotents and an \(\mathcal{H}\)-class of the finite full transformation semigroup. Semigroup Forum 84, 203–215 (2012). https://doi.org/10.1007/s00233-012-9373-7

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  • DOI: https://doi.org/10.1007/s00233-012-9373-7

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