Abstract
We consider the Stone-Čech compactification βS of a countably infinite discrete commutative semigroup S. We show that, under a certain condition satisfied by all cancellative semigroups S, the minimal right ideals of βS will belong to 2 c homeomorphism classes. We also show that the maximal groups in a given minimal left ideal will belong to 2 c homeomorphism classes. The subsets of βS of the form S + e, where e denotes an idempotent, will also belong to 2 c homeomorphism classes. All the left ideals of β N of the form β N + e , where e denotes a nonminimal idempotent of β N , will be different as right topological semigroups. If e denotes a nonminimal idempotent of β Z , e + β Z will be topologically and algebraically isomorphic to precisely one other principal right ideal of β Z defined by an idempotent: − e + βZ. The corresponding statement for left ideals is also valid.
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