CONICET | Buscador de Institutos y Recursos Humanos

A function is called algebraic on A if it is a coordinate offunction defined by a system of equations.Given an algebraic structure A, it is easy to see that every term-function of A isalgebraic on A, and that algebraic functions on A are closed under composition; thatis, they a form a clone on A. Algebraic functions can be seen as a natural generalizationof term-functions, and share some of their basic properties (e.g., they are preserved byendomorphisms and direct products).Algebraic functions have been characterized for algebras in several well-known classessuch as: Boolean Algebras, Distributive Lattices, Vector Spaces and Abelian Groups,among others. In our talk we will review these characterizations and discuss the maintools used to obtain them. We will also show how algebraic functions can be used inthe study of epimorphisms and to describe intervals in the lattice of clones over a finiteset.