IDEMPOTENT BOUNDED C-SEMIGROUPS

A semigroup with zero is idempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive a bundant semigroups. Significant to the structure of these semigroups i s that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms of double blocked Ree s matrix semigroups. This generalises Fountain's characterisation of p rimitive abundant semigroups via blocked Rees matrix semigroups [1], w hich in turn yields the Rees theorem for completely 0-simple semigroup s.