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Singular Antitone Systems

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Abstract

Given an ordered set P and an antitone map g : P → P, we obtain necessary and sufficient conditions for the existence of an odd positive integer k such that gk is isotone. The results obtained have a natural application to the dual space of an Ockham algebra. In particular, we determine the cardinality of the endomorphism semigroup of a finite subdirectly irreducible Ockham algebra.

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References

  1. Blyth, T. S. and Varlet, J. C. (1994) Ockham Algebra, Oxford University Press.

  2. McKenzie, R. N., McNulty, G. F. and Taylor, W. F. (1987) Algebras, Lattices, Varieties, Volume 1, Wadsworth & Brooks.

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Authors and Affiliations

  1. Mathematical Institute, University of St Andrews, Scotland, U.K.

    T. S. Blyth

  2. Departamento de Matemática, F.C.T., Universidade Nova de Lisboa, Portugal. E-mail

    H. J. Silva

Authors
  1. T. S. Blyth
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  2. H. J. Silva
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Blyth, T.S., Silva, H.J. Singular Antitone Systems. Order 15, 261–270 (1998). https://doi.org/10.1023/A:1006261921844

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  • DOI: https://doi.org/10.1023/A:1006261921844

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