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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Character semigroups of locally compact inverse semigroups
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by Ronald O. Fulp PDF
Proc. Amer. Math. Soc. 27 (1971), 613-618 Request permission

Abstract:

We show that if $S$ is a locally compact abelian continuous-inverse semigroup whose idempotent semigroup $E$ satisfies a certain technical condition on its prime ideals, then the maximal subgroups of the character semigroup $S^\wedge$ of $S$ are obtained as inverse limits of the duals of the maximal subgroups of $S$. It is shown that the technical conditions on $E$ are satisfied in each of the following cases: $E$ is compact, $E$ is totally disconnected, or $E$ is a chain. We then obtain necessary and sufficient conditions in order that a given inverse system of compact groups indexed by a totally disconnected semilattice $E$ admit a compatible compact semigroup topology on their disjoint union.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 613-618
  • MSC: Primary 22.05
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0276401-3
  • MathSciNet review: 0276401