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Keywords:
nearlattice; equational base
nearlattice; equational base
Summary:
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.
References:
[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 ( http://www.cs.unm.edu/mccune/prover9/)
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