## Abstract

For a class script C sign of finite lattices, the question arises whether any lattice in script C sign can be embedded into some atomistic, biatomic lattice in script C sign. We provide answers to the question above for script C sign being, respectively, - the class of all finite lattices; - the class of all finite lower bounded lattices (solved by the first author's earlier work); - the class of all finite join-semidistributive lattices (this problem was, until now, open). We solve the latter problem by finding a quasi-identity valid in all finite, atomistic, biatomic, join-semidistributive lattices but not in all finite join-semidistributive lattices.

Original language | English |
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Pages (from-to) | 31-48 |

Number of pages | 18 |

Journal | Order |

Volume | 20 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 |

## Keywords

- Atomistic
- Biatomic
- Congruence extension property
- Convex geometry
- Join-semidistributive
- Lattice
- Lower bounded

## ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics