On the ranges of algebraic functions on lattices

Studia Logica 84 (3):451 - 468 (2006)
Abstract
We study ranges of algebraic functions in lattices and in algebras, such as Łukasiewicz-Moisil algebras which are obtained by extending standard lattice signatures with unary operations.We characterize algebraic functions in such lattices having intervals as their ranges and we show that in Artinian or Noetherian lattices the requirement that every algebraic function has an interval as its range implies the distributivity of the lattice.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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Reprint years 2007
DOI 10.1007/s11225-006-9017-6
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Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.

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