ON AMENABLE RESTRICTED SEMIGROUP

O. J. OGUNSOLA, I. E. DANIEL

Abstract


We study amenability of restricted semigroup using some classes of inverse semigroups such as Clifford and Brandt semigroups. We particularly show that for a Clifford semigroup $S=\cup_{1=1}^{n}G_{i}$ with a finite set of idempotent elements, an inverse semigroup $S$ is equivalent to a restricted semigroup $S_{r}$. It was equally shown that for a restricted semigroup $S_{r}=\cup_{i\in I} S_{i}$ where $S_{i}$ is a Brandt semigroup, the amenability of a restricted semigroup is equivalent to the amenability of a Brandt semigroup.

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