Independent axiom systems for nearlattices

Araújo, João; Kinyon, Michael

http://hdl.handle.net/10400.2/3793

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Authors

Araújo, João

Kinyon, Michael

Abstract(s)

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

URI

http://hdl.handle.net/10400.2/3793

Citation

Araújo, João; Kinyon, Michael - Independent axiom systems for nearlattices. "Czechoslovak Mathematical Journal" [Em linha]. ISSN 0011-4642 (Print) 1572-9141 (Online). Vol. 61, nº 4 (Dez. 2011), p. 1-16