### 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 |

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### Keywords

- Antitone mapping
- Endomorphism semigroup
- Ockham algebra

### Cite this

*Order*,

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

}

*Order*, vol. 15, no. 3, pp. 261-270. https://doi.org/10.1023/A:1006261921844

**Singular Antitone Systems.** / Blyth, T. S.; Silva, H. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Singular Antitone Systems

AU - Blyth, T. S.

AU - Silva, H. J.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

KW - Antitone mapping

KW - Endomorphism semigroup

KW - Ockham algebra

UR - http://www.scopus.com/inward/record.url?scp=0041725532&partnerID=8YFLogxK

U2 - 10.1023/A:1006261921844

DO - 10.1023/A:1006261921844

M3 - Article

VL - 15

SP - 261

EP - 270

JO - Order-A Journal On The Theory Of Ordered Sets And Its Applications

JF - Order-A Journal On The Theory Of Ordered Sets And Its Applications

SN - 0167-8094

IS - 3

ER -