Derived Rees Matrix Semigroups as Semigroups of Transformations |
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Authors: | TS Blyth MH Almeida Santos |
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Institution: | (1) Mathematical Institute, University of St Andrews, Scotland;(2) Departamento de Matematica, F.C.T., Universidade Nova de Lisboa, Portugal |
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Abstract: | An ordered pair (e,f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent.
Previously 1] we have established that there are four distinct types of skew pairs of idempotents. We have also described
(as quotient semigroups of certain regular Rees matrix semigroups 2]) the structure of the smallest regular semigroups that
contain precisely one skew pair of each of the four types, there being to within isomorphism ten such semigroups. These we
call the derived Rees matrix semigroups. In the particular case of full transformation semigroups we proved in 3] that TX contains all four skew pairs of idempotents if and only if |X| ≥ 6. Here we prove that TX contains all ten derived Rees matrix semigroups if and only if |X| ≥ 7. |
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