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An example of a congruence distributive variety having no near-unanimity term. (English) Zbl 1132.08002

Summary: A nearlattice is a join-semilattice every principal filter of which is a lattice with respect to the induced order. Every nearlattice can be described as an algebra with one ternary operation satisfying eight simple identities. This algebra is called a nearlattice-algebra. Hence, nearlattice-algebras form a variety \({\mathcal N}\). We show that the variety \({\mathcal N}\) is congruence distributive but \({\mathcal N}\) has no near-unanimity term.

MSC:

08B10 Congruence modularity, congruence distributivity
06A12 Semilattices
08A62 Finitary algebras
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