Abstract
A nearlattice is a join semilattice such that every principal filter is a lattice with respect to the induced order. Hickman and later Chajda et al independently showed that nearlattices can be treated as varieties of algebras with a ternary operation satisfying certain axioms. Our main result is that the variety of nearlattices is 2-based, and we exhibit an explicit system of two independent identities. We also show that the original axiom systems of Hickman as well as that of Chajda et al are dependent.
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The first author was partially supported by FCT and FEDER, Project POCTI-ISFL-1- 143 of Centro de Algebra da Universidade de Lisboa, by FCT and PIDDAC through the project PTDC/MAT/69514/2006, by PTDC/MAT/69514/2006 Semigroups and Languages, and by PTDC/MAT/101993/2008 Computations in groups and semigroups.
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Araújo, J., Kinyon, M. Independent axiom systems for nearlattices. Czech Math J 61, 975–992 (2011). https://doi.org/10.1007/s10587-011-0062-6
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DOI: https://doi.org/10.1007/s10587-011-0062-6