General geometric lattices and projective geometry of modules

DOI10.1007/BF02362832zbMath0856.06006MaRDI QIDQ1912506

A. A. Lashkhi

Publication date: 11 February 1997

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

bibliographyprojective geometryprincipal ideal domainscontinuous geometrysubmodule latticegeometric latticesquotient latticelattice-geometric theory of modules

Mathematics Subject Classification ID

Representation theory of lattices (06B15) Semimodular lattices, geometric lattices (06C10) Complemented modular lattices, continuous geometries (06C20) General module theory in associative algebras (16D10) Lattices of subspaces and geometric closure systems (51D25) Research exposition (monographs, survey articles) pertaining to geometry (51-02) Research exposition (monographs, survey articles) pertaining to ordered structures (06-02)

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Cites Work

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• On the representation of complemented modular lattices
• Relation algebras and projective geometries
• Fundamental theorem of projective geometry in Lie modules and algebras
• Subprojective lattices and projective geometry
• Splitting algebras and a weak notion of projectivity
• Universal Horn axiom systems for lattices of submodules
• Über die Struktursätze der projektiven Geometrie
• Ein Struktursatz für ebene Verbände
• On coordinates in modular lattices with a homogeneous basis
• Section semicomplemented lattices
• Uniforme Hjelmslev-Ebenen und modulare Verbände
• Representations of primary Arguesian lattices
• Desargues' law and the representation of primary lattices
• Verbandstheoretische Charakterisierung n-stufiger Geometrien
• Geometric aspects of primary lattices
• The amalgamation property in equational classes of modular lattices
• A lattice formulation for transcendence degrees and p-bases
• On the transitivity of perspective mappings
• Zur Axiomatik der projektiven ebenen Ringgeometrien. 1. Tl
• On lattice theoretic characterization of the parallelism in affine geometry
• The representation of relational algebras
• The projective space
• Any orthocomplemented complete modular lattice is a continuous geometry
• Projective Geometries as Projective Modular Lattices
• On The Coordinatization Theorem Of J. Von Neumann
• Von Neumann and lattice theory
• Introduction to Von Neumann Algebras and Continuous Geometry
• Representations of Complemented Modular Lattices
• A SIMPLIFIED PROOF OF VON NEUMANN'S COORDINATIZATION THEOREM
• Representation of Modular Lattices and Of Relation Algebras
• On the Arithmetic of Projective Coordinate Systems
• The Coordinatization of Arguesian Lattices
• The Variety of Modular Lattices is Not Generated by its Finite Members
• In Search of a Pappian Lattice Identity
• Projective Geometry on Partially Ordered Sets
• On the Representation of Lattices by Modules
• On the Abstract Properties of Linear Dependence
• The Slimmest Geometric Lattices
• An Introduction to Matroid Theory
• Lectures on matroids
• Characterizations of Finite Projective and Affine Spaces
• Projektive Hjelmslevräume.
• Lattice Isomorphisms between Modules (1) Endomorphism Rings^∗
• Examples of Continuous Geometries
• Some Interpretations of Abstract Linear Dependence in Terms of Projective Geometry
• Algebraic Theory of Continuous Geometries
• On incidence geometry
• Representations of Lattices by Sets
• On the Foundations of Inversion Geometry
• On the representation of lattices
• Complemented Modular Lattices and Projective Spaces of Infinite Dimension
• Modularity in Birkhoff lattices
• Null systems in projective space
• A Unified Theory of Projective Spaces and Finite Abelian Groups