### Abstract

Given any Ockham algebra, we describe the congruences such that the quotient algebras are boolean. This description is obtained using certain ideals that we call pro-boolean ideals. We prove that every proper pro-boolean ideal is the intersection of a family of falsity ideals. We also determine when every proper pro-boolean ideal is a unique intersection of such ideals. Finally, we show that if an Ockham algebra in the Urquhart class P n+2,n is fixed point free then the corresponding dual space has a fixed point. This result is a natural generalisation of a well known theorem (Blyth, T. S., Varlet, J. C. (1994). Ockham Algebras. Oxford University Press, Theorem 6.3).

Original language | English |
---|---|

Pages (from-to) | 5391-5404 |

Journal | Communications in Algebra |

Volume | 31 |

Issue number | 11 |

DOIs | |

Publication status | Published - 31 Aug 2006 |

### Fingerprint

### Keywords

- Ockham algebra
- pro-boolean ideal
- Congruence
- Falsity ideal