CONICET | Buscador de Institutos y Recursos Humanos

A function is called algebraic on A if it is one of the functions defined by asystem of equations in A. For example, the complement function is algebraic on the two-element bounded lattice, as witnessed by the systemx ∧ z = 0x ∨ z = 1.Given an algebraic structure A, it is easy to see that every term-function of A is algebraic on A, and that algebraic functions on A are closed under composition; that is, they a form a clone on A. Algebraic functions can be seen as a natural generalization of term-functions, and share some of their basic properties (e.g., they are preserved by endomorphisms and direct products).Algebraic functions have been characterized for algebras in several well-known classes such as: Boolean Algebras, Distributive Lattices, Vector Spacesand Abelian Groups, among others. In our talk we will review these characteri-zations and discuss the main tools used to obtain them. We will also show howalgebraic functions can be used in the study of epimorphisms and to describeintervals in the lattice of clones over a finite set