Studia Logica

, Volume 98, Issue 1–2, pp 285–306

Algebraic Functions

Article

Abstract

Let A be an algebra. We say that the functions f1, . . . , fm : AnA are algebraic on A provided there is a finite system of term-equalities \({{\bigwedge t_{k}(\overline{x}, \overline{z}) = s_{k}(\overline{x}, \overline{z})}}\) satisfying that for each \({{\overline{a} \in A^{n}}}\), the m-tuple \({{(f_{1}(\overline{a}), \ldots , f_{m}(\overline{a}))}}\) is the unique solution in Am to the system \({{\bigwedge t_{k}(\overline{a}, \overline{z}) = s_{k}(\overline{a}, \overline{z})}}\). In this work we present a collection of general tools for the study of algebraic functions, and apply them to obtain characterizations for algebraic functions on distributive lattices, Stone algebras, finite abelian groups and vector spaces, among other well known algebraic structures.

Keywords

Implicit equational definition Distributive Lattice Stone Algebra 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Facultad de Matemática, Astronomía y Física (Fa.M.A.F.)Universidad Nacional de CórdobaCórdobaArgentina

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