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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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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest, Romania

    Sergiu Rudeanu

  2. Dept. of Computer Science, University of Massachusetts Boston, 100 Morrissey Blvd., Boston, USA

    Dan A. Simovici

Authors
  1. Sergiu Rudeanu
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  2. Dan A. Simovici
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Correspondence to Sergiu Rudeanu.

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Presented by Daniele Mundici

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Rudeanu, S., Simovici, D.A. On the Ranges of Algebraic Functions on Lattices. Stud Logica 84, 451–468 (2006). https://doi.org/10.1007/s11225-006-9017-6

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  • DOI: https://doi.org/10.1007/s11225-006-9017-6

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