Semidistributivity and whitman property in implication zroupoids

DOI10.1515/ms-2021-0056zbMath1491.06037arXiv2009.07978OpenAlexW3085802105MaRDI QIDQ2063346

Hanamantagouda P. Sankappanavar, Juan Manuel Cornejo

Publication date: 11 January 2022

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.07978

zbMATH Keywords

semilatticeDe Morgan algebraimplication zroupoidsemidistributivityBirkhoff bisemigroupBirkhoff identitywhitman property

Mathematics Subject Classification ID

Lattices of varieties (08B15) Equational logic, Mal'tsev conditions (08B05) Other algebras related to logic (03G25) De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) (06D30) Other generalizations of distributive lattices (06D75)

Uses Software

• Prover9
• Mace4

Cites Work

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• Order in implication zroupoids
• On implicator groupoids
• The lattice of varieties of implication semigroups
• Semigroups with \(\wedge\)-semidistributive subsemigroup lattices
• An algebraic approach to non-classical logics
• Splitting lattices generate all lattices
• On derived algebras and subvarieties of implication zroupoids
• Symmetric implication zroupoids and identities of Bol-Moufang type
• Symmetric implication zroupoids and weak associative laws
• Semisimple varieties of implication zroupoids
• Semidistributive inverse semigroups
• Finite Sublattices of a Free Lattice
• A Set of Four Postulates for Boolean Algebra in Terms of the "Implicative" Operation
• Congruence Relations in Semi-Lattices
• Sublattices of a Free Lattice
• Implication Zroupoids and Identities of Associative Type
• On distributive quad-lattices

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