Right ideal decompositions of G⁎

Abstract

Let G be an infinite discrete group, let βG be the Stone–Čech compactification of G, and let G⁎=βG∖G. We show that if G can be embedded algebraically in a compact zero dimensional second countable group (in particular, if G=Z), then there are a decomposition D of G⁎ into right ideals of βG and a closed subsemigroup T of G⁎ containing all the idempotents such that DT={R∩T:R∈D} is a decomposition of T into closed right ideals and T/DT is homeomorphic to ω⁎.