### 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 g^{k} 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.

Original language | English |
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Pages (from-to) | 261-270 |

Number of pages | 10 |

Journal | Order |

Volume | 15 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1998 |

### Keywords

- Antitone mapping
- Endomorphism semigroup
- Ockham algebra

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## Cite this

Blyth, T. S., & Silva, H. J. (1998). Singular Antitone Systems.

*Order*,*15*(3), 261-270. https://doi.org/10.1023/A:1006261921844