| 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.
Mathematics Subject Classifications (2000) Primary 06A12, 06C99, 08B26. |
