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Congruence relations on cone semigroups

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Abstract

Since closed cones C in finite dimensional real vector spaces V play the role of “Lie algebras” for finite dimensional compact abelian semigroups, we discuss the structure of congruence relations on such cones. We show in particular that a monotone closed congruence on such a cone C is entirely determined by a countable collection of closed ideals of C and a countable collection of linear subspaces of V (see theorem 3.3).

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Authors and Affiliations

  1. Faculté des Sciences, Parc Grandmont, 37, Tours, (France)

    Klaus Keimel

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  1. Klaus Keimel
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Additional information

Communicated by H. K. Hofmann

An address delivered at the Second Florida Symposium on Automata and Semigroups, University of Florida, Gainesville, Florida, April 13–16, 1971.

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Keimel, K. Congruence relations on cone semigroups. Semigroup Forum 3, 130–147 (1971). https://doi.org/10.1007/BF02572953

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  • DOI: https://doi.org/10.1007/BF02572953

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