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

Higgins, Peter M (2012) 'The product of the idempotents and an $\mathcal{H}$ -class of the finite full transformation semigroup.' Semigroup Forum, 84 (2). pp. 203-215. ISSN 0037-1912

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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 H-class of T X. We show that S is a semigroup and is a union of 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 Reg(S) forms a right ideal of S. © 2012 Springer Science+Business Media, LLC.

Item Type: Article Full transformation semigroup; Idempotents; H-class; Hall's Lemma Q Science > QA Mathematics Faculty of Science and HealthFaculty of Science and Health > Mathematical Sciences, Department of Elements Elements 12 Feb 2013 13:05 15 Jan 2022 00:29 http://repository.essex.ac.uk/id/eprint/5514