Embedding Finite Lattices into Finite Biatomic Lattices

Kira Adaricheva, Friedrich Wehrung

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)31-48
Number of pages18
JournalOrder
Volume20
Issue number1
DOIs
Publication statusPublished - 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

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