On the Ranges of Algebraic Functions on Lattices |
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| Authors: | Sergiu Rudeanu Dan A. Simovici |
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| Affiliation: | (1) Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest, Romania;(2) Dept. of Computer Science, University of Massachusetts Boston, 100 Morrissey Blvd., Boston, USA |
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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. Presented by Daniele Mundici |
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| Keywords: | Ł ukasiewicz-Moisil algebras determination principle modular lattice distributive lattice |
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