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On the ranges of algebraic functions on lattices. (English) Zbl 1114.03052

The main goal of the present paper is to study ranges of algebraic functions in lattices and in some particular algebras, such as Łukasiewicz-Moisil algebras, which are obtained by extending standard lattice signatures with unary operations. The authors characterize algebraic functions in such lattices having intervals as their ranges. Also, they prove that an Artinian or Noetherian lattice which satisfies the property that every algebraic function has an interval as its range is distributive (see Theorem 3.1).

MSC:

03G10 Logical aspects of lattices and related structures
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
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