On topological McAlister semigroups

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

In this paper we investigate algebraic and topological properties of McAlister semigroups. We show that for a non-zero cardinal λ the group of automorphisms of the McAlister semigroup M λ is isomorphic to the direct product Sym(λ)×Z 2, where Sym(λ) is the group of permutations of λ. McAlister semigroups admit a unique compact Hausdorff semigroup topology. Each non-zero element of a Hausdorff semitopological McAlister semigroup is isolated. It follows that the free inverse semigroup over a singleton admits only the discrete Hausdorff shift-continuous topology. We prove that a Hausdorff locally compact semitopological semigroup M 1 is either compact or discrete. However, this dichotomy does not hold for the semigroup M 2. Moreover, M 2 admits continuum many different Hausdorff locally compact inverse semigroup topologies.

OriginalspracheEnglisch
Aufsatznummer107274
FachzeitschriftJournal of Pure and Applied Algebra
Jahrgang227
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - Apr. 2023

ÖFOS 2012

  • 101001 Algebra
  • 101022 Topologie

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