Congruence modularity implies the Arguesian identity

DOI10.1007/BF02485830zbMath0354.08008MaRDI QIDQ1236560

Ralph Freese, Bjarni Jónsson

Publication date: 1976

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

Mathematics Subject Classification ID

Modular lattices, Desarguesian lattices (06C05) Varieties (08B99)

Related Items (25)

A perspective on algebraic representations of lattices ⋮ Directions in lattice theory ⋮ Jónsson's contributions to lattice theory ⋮ Finitely based modular congruence varietes are distributive ⋮ On the Arithmetic of Projective Coordinate Systems ⋮ Frames and rings in congruence modular varieties ⋮ Alan Day's early work: Congruence identities ⋮ Alan Day's work on modular and arguesian lattices ⋮ Projective Geometries as Projective Modular Lattices ⋮ The Little Desarguesian Theorem for Algebras in Modular Varieties ⋮ A review of some of Bjarni Jónsson's results on representation of Arguesian lattices ⋮ A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity ⋮ Residually Small Varieties with Modular Congruence Lattices ⋮ Finitely based congruence varieties ⋮ On Freese’s technique ⋮ General lattice theory: 1979 problem update ⋮ On some identities valid in modular congruence varieties ⋮ Bibliography on quantum logics and related structures ⋮ Tribute to Bjarni Jónsson ⋮ On embedding lattices into block lattices of regular algebras and groups ⋮ Relation identities in 3-distributive varieties ⋮ A test for identities satisfied in lattices of submodules ⋮ The shape of congruence lattices ⋮ Congruence modularity implies the Arguesian law for single algebras with a difference term ⋮ On Jónsson's theorem

Cites Work

• Unnamed Item
• Varieties whose congruences satisfy certain lattice identities
• The class of Arguesian lattices is self-dual
• The amalgamation property in equational classes of modular lattices

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