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, Volume 21, Issue 3, pp 257–263 | Cite as

Semilattice Operations Generated by Lattice Terms

  • R. Padmanabhan
  • P. Penner
Article
  • 33 Downloads

Abstract

Let ℒ=〈L;∨,∧〉 be a subdirectly irreducible modular lattice, cL 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.

Keywords

semilattice lattice quasilattice compatible orders subdirectly irreducible distributive multisemilattice modular lattice pseudomedian algebras 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada

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