Sublattices of lattices of order-convex sets. I: The main representation theorem

DOI10.1016/j.jalgebra.2004.01.023zbMath1063.06003arXivmath/0501341OpenAlexW1965260120MaRDI QIDQ1882895

Friedrich Wehrung, M. V. Schwidefsky

Publication date: 1 October 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501341

zbMATH Keywords

embeddingpartially ordered setlattice identitiesjoin-semidistributivityorder-convex set

Mathematics Subject Classification ID

Partial orders, general (06A06) Representation theory of lattices (06B15) Varieties of lattices (06B20)

Related Items (8)

Lattices of order-convex sets of forests ⋮ ON LATTICES EMBEDDABLE INTO LATTICES OF ORDER-CONVEX SETS: CASE OF TREES ⋮ Varieties of lattices with geometric descriptions ⋮ On lattices embeddable into lattices of order-convex sets. II: Star-like posets ⋮ Algebraic Methods for Granular Rough Sets ⋮ The lattice of convex subsets of a monounary algebra ⋮ Characterizations of the convex geometries arising from the double shellings of posets ⋮ Embedding lattices into derived lattices.

Uses Software

• HERWIG 5.1

Cites Work

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• The theory of convex geometries
• The convexity lattice of a poset
• Meet-distributive lattices and the anti-exchange closure
• Two embedding theorems for lower bounded lattices
• Algebraic point lattices of quasivarieties
• Join-semidistributive lattices and convex geometries.
• Varieties of Lattices
• SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, II.
• SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, III: THE CASE OF TOTALLY ORDERED SETS
• Complemented Modular Lattices and Projective Spaces of Infinite Dimension
• The decision problem for some classes of sentences without quantifiers

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