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Semilattice Operations Generated by Lattice Terms

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Abstract

Let ℒ=〈L;∨,∧〉 be a subdirectly irreducible modular lattice, c∈L and p(x,y,z) an essentially ternary lattice term. In this paper we show that if p(x,y,c) is a semilattice operation then p(x,y,c)=∨ or ∧ and L is bounded and c=0 or c=1. This sheds light on the methodology used to move back and forth between generalizations of median algebras and lattices, and provides a negative answer to a problem posed by A. Knoebel and G. Meletiou.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    R. Padmanabhan & P. Penner

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  1. R. Padmanabhan
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  2. P. Penner
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Correspondence to R. Padmanabhan.

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Mathematics Subject Classifications (2000)

Primary 06A12, 06C99, 08B26.

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Padmanabhan, R., Penner, P. Semilattice Operations Generated by Lattice Terms. Order 21, 257–263 (2004). https://doi.org/10.1007/s11083-004-0024-9

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  • DOI: https://doi.org/10.1007/s11083-004-0024-9

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