Finite equational bases for congruence modular varieties

DOI10.1007/BF01195263zbMath0648.08006MaRDI QIDQ1104959

Ralph McKenzie

Publication date: 1987

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

zbMATH Keywords

congruence modular varietycommutatorslocally finite varietyfinite axiomatizabilityresidually smallfinite equational basis

Mathematics Subject Classification ID

Congruence modularity, congruence distributivity (08B10)

Related Items (24)

Inherently nonfinitely based lattices ⋮ Bjarni Jónsson's contributions in algebra ⋮ Identities and quasi-identities of pointed algebras ⋮ Unnamed Item ⋮ The variety generated by \(\mathbb {A}(\mathcal {T})\) -- two counterexamples ⋮ Finite axiomatizability of congruence rich varieties ⋮ Nilpotent and solvable radicals in locally finite congruence modular varieties ⋮ Relatively congruence modular quasivarieties of modules ⋮ Universal algebraic methods for non-classical logics ⋮ Lyndon's groupoid is not inherently nonfinitely based ⋮ Triangular irreducibility of congruences in quasivarieties ⋮ Universal algebras ⋮ Neutrabelian algebras ⋮ A juggler's dozen of easy\(^\dag\) problems (\(^\dag\) Well, easily formulated \dots). ⋮ A field guide to equational logic ⋮ Embedding general algebras into modules ⋮ Finite basis problems and results for quasivarieties ⋮ COMPUTATIONAL COMPLEXITY OF THE FINITE ALGEBRA MEMBERSHIP PROBLEM FOR VARIETIES ⋮ Commutator Theory for Relatively Modular Quasivarieties ⋮ A finite basis theorem for difference-term varieties with a finite residual bound ⋮ A finite basis theorem for residually finite, congruence meet-semidistributive varieties ⋮ Finite Basis Theorems for Relatively Congruence-Distributive Quasivarieties ⋮ FREGEAN VARIETIES ⋮ A Characterization of Finitely Decidable Congruence Modular Varieties

Cites Work

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• Nilpotent and solvable radicals in locally finite congruence modular varieties
• An easy way to the commutator in modular varieties
• Congruence modularity is permutability composed with distributivity
• Finite equational bases for finite algebras in a congruence-distributive equational class
• Baker's finite basis theorem
• Identities of finite algebras
• The Laws of Finite Pointed Groups
• Residually Small Varieties with Modular Congruence Lattices
• The structure of finite algebras

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