Adaricheva, K. and Maróti, Miklós and McKenzie, R. and Nation, J. B. and Zenk, E. R.
(2006)
*The Jónsson-Kiefer Property.*
Studia Logica, 83 (1-3).
pp. 111-131.
ISSN 0039-3215

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## Abstract

The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2(ℵ0), or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that has no meet-prime element or join-prime element. This lattice L has |L| = |LC| = 2(ℵ0) where L(c) is the set of compact elements of L.

Item Type: | Article |
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Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |

Depositing User: | Erika Bilicsi |

Date Deposited: | 04 Apr 2013 08:56 |

Last Modified: | 04 Apr 2013 08:56 |

URI: | http://real.mtak.hu/id/eprint/4591 |

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