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On the Ranges of Algebraic Functions on Lattices

Sergiu Rudeanu and Dan A. Simovici
Studia Logica: An International Journal for Symbolic Logic
Vol. 84, No. 3 (Dec., 2006), pp. 451-468
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016844
Page Count: 18
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On the Ranges of Algebraic Functions on Lattices
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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.

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