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Proceedings of the American Mathematical Society

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

 

 

Character semigroups of locally compact inverse semigroups


Author: Ronald O. Fulp
Journal: Proc. Amer. Math. Soc. 27 (1971), 613-618
MSC: Primary 22.05
MathSciNet review: 0276401
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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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DOI: https://doi.org/10.1090/S0002-9939-1971-0276401-3
Keywords: Locally compact abelian semigroups, character semigroups, inverse limits, duals of maximal groups, compact topologies, totally disconnected semilattices
Article copyright: © Copyright 1971 American Mathematical Society