Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 975-992, 2011

Independent axiom systems for nearlattices

João Araújo, Michael Kinyon

João Araújo, Universidade Aberta and Centro de Álgebra, Universidade de Lisboa, 1649-003 Lisboa, Portugal, e-mail: jaraujo@ptmat.fc.ul.pt; Michael Kinyon, Department of Mathematics, University of Denver, 2360 S Gaylord St, Denver, Colorado 80208 USA, e-mail: mkinyon@math.du.edu

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.

Keywords: nearlattice, equational base

Classification (MSC 2010): 06A12, 06B75


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