On the ranges of algebraic functions on lattices

Studia Logica 84 (3):451 - 468 (2006)
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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DOI 10.2307/20016844
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Garrett Birkhoff (1940). Lattice Theory. Journal of Symbolic Logic 5 (4):155-157.
George Grätzer (1982). Universal Algebra. Studia Logica 41 (4):430-431.

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