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nearlattice; equational base
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.
[1] Chajda, I., Halaš, R.: An example of a congruence distributive variety having no near-unanimity term. Acta Univ. M. Belii Ser. Math. 13 (2006), 29-31. MR 2353310
[2] Chajda, I., Halaš, R., Kühr, J.: Semilattice structures. Research and Exposition in Mathematics 30, Heldermann Verlag, Lemgo (2007). MR 2326262
[3] Chajda, I., Kolařík, M.: Nearlattices. Discrete Math. 308 (2008), 4906-4913. DOI 10.1016/j.disc.2007.09.009 | MR 2446101
[4] Hickman, R.: Join algebras. Commun. Algebra 8 (1980), 1653-1685. DOI 10.1080/00927878008822537 | MR 0585925 | Zbl 0436.06003
[5] McCune, W.: Prover9 and Mace4, version 2009-11A. \hfil (
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