Algebraic and topological equivalences in the Stone-Čech compactification of a discrete semigroup (Q1902998)

The authors study idempotents and minimal right ideals in the induced right topological semigroup structure of the Stone-Čech compactification \(\beta (S)\) of a countably infinite (discrete) commutative semigroup \(S\). Under certain conditions which are satisfied by all cancellative semigroups \(S\), it is shown that the minimal right ideals of \(S\) form \(2^c\) homeomorphism classes. A similar statement holds for the maximal groups in a given minimal left ideal. All left ideals of \(\beta N\) of the form \(\beta N + e\), where \(e\) is a nonminimal idempotent, are non-isomorphic as right topological semigroups. In \(\beta Z\) only \(-e + \beta Z\) is topologically isomorphic to \(e + \beta Z\), and a similar statement holds for left ideals.