Finitely related clones and algebras with cube terms.

DOI10.1007/s11083-011-9232-2zbMath1310.08002OpenAlexW2054605362MaRDI QIDQ438817

Petar Marković, Miklós Maróti, Ralph McKenzie

Publication date: 31 July 2012

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11083-011-9232-2

zbMATH Keywords

polynomial-time algorithmsalgebras with few subpowerscube termsfinite idempotent algebrasfinitely related clonesValeriote conjecture

Mathematics Subject Classification ID

Equational logic, Mal'tsev conditions (08B05) Operations and polynomials in algebraic structures, primal algebras (08A40) Congruence modularity, congruence distributivity (08B10) Finitary algebras (08A62) Word problems (aspects of algebraic structures) (08A50)

Related Items (18)

Naturally dualizable algebras omitting types 1 and 5 have a cube term ⋮ Preserving near unanimity terms under products ⋮ Finite bands are finitely related ⋮ Promise Constraint Satisfaction: Algebraic Structure and a Symmetric Boolean Dichotomy ⋮ Cube term blockers without finiteness ⋮ On finite Taylor algebras ⋮ Not all nilpotent monoids are finitely related ⋮ On finitely related semigroups. ⋮ Unnamed Item ⋮ Existence of cube terms in finite algebras ⋮ Mal'tsev conditions, lack of absorption, and solvability. ⋮ Maltsev families of varieties closed under join or Maltsev product ⋮ On the number of clonoids ⋮ Taylor's modularity conjecture and related problems for idempotent varieties ⋮ Deciding absorption ⋮ The number of clones determined by disjunctions of unary relations ⋮ Topological Birkhoff ⋮ Testing for edge terms is decidable

Cites Work

• Unnamed Item
• Cyclic terms for \(\text{SD}_{\vee}\) varieties revisited
• Finite degree: algebras in general and semigroups in particular
• Few subpowers, congruence distributivity and near-unanimity terms
• Varieties with few subalgebras of powers
• A Subalgebra Intersection Property for Congruence Distributive Varieties
• Tractability and Learnability Arising from Algebras with Few Subpowers

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