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Media type:
E-Article
Title:
On the Ranges of Algebraic Functions on Lattices
Contributor:
Rudeanu, Sergiu;
Simovici, Dan A.
Published:
Springer, 2006
Published in:
Studia Logica: An International Journal for Symbolic Logic, 84 (2006) 3, Seite 451-468
Language:
English
ISSN:
0039-3215;
1572-8730
Origination:
Footnote:
Description:
<p>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.</p>