The universal semilattice compactification of a semigroup

Abstract

The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group.

Rectangular group compactification of a semigroup

“…In recent years there has been considerable interest in studying those function algebras on a semitopological semigroup whose associated semigroup compactifications are universal with respect to some substantial properties. For instance, see [2], [3], [5] and references therein, specially Berglund et al [1]. Following the above mentioned papers, in this paper after some observations on the algebraic theory of simple semigroups and also rectangular groups, we introduce a function algebra RG(S) on a semitopological semigroup S and as the main goal we show that RG-compactification of S is the largest rectangular compactification of S.…”