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. DOI https://doi.org/10.1007/s00233-012-9373-7
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. DOI https://doi.org/10.1007/s00233-012-9373-7
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. DOI https://doi.org/10.1007/s00233-012-9373-7
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 |
|---|---|
| Uncontrolled Keywords: | Full transformation semigroup; Idempotents; H-class; Hall's Lemma |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 12 Feb 2013 13:05 |
| Last Modified: | 04 Dec 2024 06:22 |
| URI: | http://repository.essex.ac.uk/id/eprint/5514 |