A geometric description of modular lattices

DOI10.1007/BF01221792zbMath0816.06008MaRDI QIDQ1327460

Douglas Pickering, Christian Herrmann, Micheale Susan Roddy

Publication date: 23 July 1995

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

zbMATH Keywords

order ideals2-distributive latticessubspace latticesordered projective spacesspatial modular lattices

Mathematics Subject Classification ID

Lattices of varieties (08B15) Structure and representation theory of distributive lattices (06D05) General theory of linear incidence geometry and projective geometries (51A05) Modular lattices, Desarguesian lattices (06C05) Varieties of lattices (06B20)

Related Items (17)

On locally finite modular lattice varieties of finite height ⋮ Alan Day's work on modular and arguesian lattices ⋮ The minimal number of join irreducibles of a finite modular lattice ⋮ Finitely based congruence varieties ⋮ Varieties of lattices with geometric descriptions ⋮ SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, III: THE CASE OF TOTALLY ORDERED SETS ⋮ On the contraction of vectorial lattice representations ⋮ Weakly submodular rank functions, supermatroids, and the flat lattice of a distributive super\-matroid ⋮ On the number of join irreducibles and acyclicity in finite modular lattices ⋮ A compact representation for modular semilattices and its applications ⋮ Cover preserving embedding of modular lattices into partition lattices ⋮ Tight embedding of modular lattices into partition lattices: progress and program ⋮ VON NEUMANN COORDINATIZATION IS NOT FIRST-ORDER ⋮ Rank axiom of modular supermatroids: a connection with directional DR submodular functions ⋮ Small non-Arguesian lattices ⋮ Join-semidistributive lattices and convex geometries. ⋮ Enumerating maximal consistent closed sets in closure systems

Cites Work

• Diagrams for modular lattices
• Biatomic lattices
• Frink's theorem for modular lattices
• Finite sublattices of four-generated modular lattices
• The core of finite lattices
• On free modular lattices generated by finite chains
• Ideal lattices of lattices
• Zum Wortproblem für freie Untermodulverbände
• A test for identities satisfied in lattices of submodules
• Acyclic modular lattices and their representations
• Equational classes of lattices
• Equational Classes of Lattices.
• A Unified Theory of Projective Spaces and Finite Abelian Groups
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