On compact divisible abelian semigroups

Abstract

The algebraic structure of divisible abelian semigroups has been studied in [9] and [1]. Some results on the topological and algebraic structure of compact uniquely divisible abelian semigroups have been obtained in [4] and [5]. A statement of equivalent conditions for a compact abelian semigroup to be divisible is presented in the present paper. Some of the results in [4] are extended to subunithetic semigroups, which are the fundamental building blocks of a divisible abelian semigroup.