ON REES MATRIX REPRESENTATIONS OF ABUNDANT SEMIGROUPS WITH ADEQUATE TRANSVERSALS

The concepts of ⁄-relation of a (i-)semigroup and "-adequate transversal of a (i-)abundant semigroup are deflned in this note. Then we develop a matrix type theory for abundant semigroups. We give some equivalent conditions of a Rees matrix semigroup being abundant and some equivalent conditions of an abundant Rees matrix semigroup having an adequate transversal. Then we obtain some Rees matrix representa- tions for abundant semigroups with adequate transversals by the above theories.