Construction of right topological compactifications for discrete versions of subsemigroups of compact groups (Q1115979)

In [ibid. 35, 207-225 (1987; Zbl 0615.22002)], \textit{J. Pym} constructed right topological compactifications for discrete versions of subsemigroups of compact groups that are of simple algebraic structure but are rather sophisticated topologically. In this paper, a relatively short, direct, and more transparent construction of the same compactifications is presented, using as a tool nothing but the existence of Stone-Čech compactifications. Various characterizations for the compactifications to the semitopological are obtained.