Geodesic
Independent axiom systems for nearlattices
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 975-992
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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.
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.
DOI : 10.1007/s10587-011-0062-6
Classification : 06A12, 06B75, 68T15
Keywords: nearlattice; equational base 
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Araújo, João; Kinyon, Michael. Independent axiom systems for nearlattices. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 975-992. doi: 10.1007/s10587-011-0062-6

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