LATTICES OF QUASI-EQUATIONAL THEORIES AS CONGRUENCE LATTICES OF SEMILATTICES WITH OPERATORS: PART I

DOI10.1142/S0218196712500658zbMath1284.08018arXiv1106.2203MaRDI QIDQ4902684

J. B. Nation, K. V. Adaricheva

Publication date: 17 January 2013

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2203

zbMATH Keywords

congruence latticesemilatticequasivarietyquasi-equational theorylattice of quasivarieties

Mathematics Subject Classification ID

Subalgebras, congruence relations (08A30) Quasivarieties (08C15) Semilattices (06A12)

Related Items (3)

Lattices of theories in languages without equality ⋮ Quasivariety lattices of pointed abelian groups. ⋮ A topological duality for monotone expansions of semilattices

Cites Work

• Equational closure operator and forbidden semidistributive lattices
• Equational theories as congruences of enriched monoids
• Axiomatizable and nonaxiomatizable congruence prevarieties
• The cardinality of subdirectly indecomposable systems in quasivarieties
• A property of the lattice of equational theories
• On atoms in the lattice of quasivarieties
• Weak distributive laws and their role in lattices of congruences and equational theories
• A class of lattices of quasivarities
• Further properties of lattices of equational theories
• Intervals in the lattice of varieties
• The structure of the lattices of quasivarieties
• Open questions related to the problem of Birkhoff and Maltsev
• Lattices of equational theories are congruence lattices of monoids with one additional unary operation
• The Pontryagin duality of compact O-dimensional semilattices and its applications
• Congruence lattices of semilattices
• Join-semidistributive lattices and convex geometries.
• Lattices of algebraic subsets

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