Congruence modularity is permutability composed with distributivity

DOI10.1007/BF01223741zbMath0465.08005OpenAlexW2095206903MaRDI QIDQ1154493

H. Peter Gumm

Publication date: 1981

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01223741

zbMATH Keywords

congruence modularitymodular varietylattices of congruencesMal'cev type conditionpermutability of congruences

Mathematics Subject Classification ID

Equational logic, Mal'tsev conditions (08B05) Congruence modularity, congruence distributivity (08B10)

Related Items (26)

Bjarni Jónsson's contributions in algebra ⋮ Algebraic properties and dismantlability of finite posets ⋮ Finite equational bases for congruence modular varieties ⋮ Nilpotent and solvable radicals in locally finite congruence modular varieties ⋮ The Jónsson distributivity spectrum ⋮ Quasiorder lattices of varieties ⋮ Absorption and directed Jónsson terms ⋮ The Gumm level equals the Alvin level in congruence distributive varieties ⋮ Congruence-distributive varieties of algebras ⋮ An easy test for congruence modularity ⋮ Equations implying congruence \(n\)-permutability and semidistributivity. ⋮ Monotone clones and congruence modularity ⋮ Categorical (binary) difference terms and protomodularity ⋮ The Tschantz and the Alvin higher conditions are equivalent in congruence distributive varieties ⋮ The modular commutator via the Gumm terms ⋮ On supernilpotent algebras ⋮ Finitary decidability implies congruence permutability for congruence modular varieties ⋮ A finite basis theorem for difference-term varieties with a finite residual bound ⋮ Congruence lower semimodularity and 2-finiteness imply congruence modularity ⋮ Pseudo‐loop conditions ⋮ Random models of idempotent linear Maltsev conditions. I. Idemprimality ⋮ ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS ⋮ On difunctionality of class relations ⋮ Formations, bihomorphisms and natural transformations ⋮ A new proof of Gumm's theorem ⋮ Unnamed Item

Cites Work

• A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity
• An easy way to the commutator in modular varieties
• Algebras Whose Congruence Lattices are Distributive.
• A Characterization of Modularity for Congruence Lattices of Algebras*
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