On congruence lattices of lattices

DOI10.1007/BF02033636zbMath0101.02103MaRDI QIDQ5895977

E. Tamás Schmidt, George Grätzer

Publication date: 1962

Published in: Acta Mathematica Academiae Scientiarum Hungaricae (Search for Journal in Brave)

zbMATH Keywords

fieldsringslattices

Related Items (36)

Congruence lattices of finite \(p\)-algebras ⋮ Unnamed Item ⋮ Congruence lattices of \(p\)-algebras ⋮ My collaboration with E. T. Schmidt spanning six decades ⋮ A convex combinatorial property of compact sets in the plane and its roots in lattice theory ⋮ Some preliminary results on the set of principal congruences of a finite lattice ⋮ The order of principal congruences of a bounded lattice ⋮ Unnamed Item ⋮ Compatible Relations of Modular and Orthomodular Lattices ⋮ Representing an isotone map between two bounded ordered sets by principal lattice congruences ⋮ CLOSURE OPERATORS, FRAMES AND NEATEST REPRESENTATIONS ⋮ Complete congruence lattices of two related modular lattices ⋮ Injective and projective semimodules over involutive semirings ⋮ Strongly reflexive lattices ⋮ The graphs of join-semilattices and the shape of congruence lattices of particle lattices ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A solution to Dilworth's congruence lattice problem ⋮ An extension theorem for planar semimodular lattices. ⋮ Non-representable distributive semilattices ⋮ Conjunctive join-semilattices ⋮ Representing some families of monotone maps by principal lattice congruences ⋮ Notes on sectionally complemented lattices. IV: How far does the atom lemma go? ⋮ CONGRUENCE FD-MAXIMAL VARIETIES OF ALGEBRAS ⋮ Finite distributive lattices are congruence lattices of almost-geometric lattices ⋮ Congruence lattices of planar lattices ⋮ On the length of the congruence lattice of a lattice ⋮ On the largest numbers of congruences of finite lattices ⋮ On the length of the congruence lattice of a lattice ⋮ Representing congruence lattices of lattices with partial unary operations as congruence lattices of lattices. II: Interval ordering ⋮ Dependence of finiteness conditions in distributive lattices ⋮ The submodule lattice of a cyclic module ⋮ Some combinatorial aspects of congruence lattice representations ⋮ Modular and Distributive Semilattices ⋮ The strong independence theorem for automorphism groups and congruence lattices of arbitrary lattices ⋮ Unnamed Item

Cites Work

• Lattices whose congruences form a Boolean algebra
• Theory of equivalence relations
• Ideals and congruence relations in lattices
• Standard ideals in lattices
• Representations of Lattices by Sets
• On a characterization of the lattice of all ideals of a Boolean ring
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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