Algebraic functions in quasiprimal algebras

Abstract

A function is algebraic on an algebra A if it can be implicitly defined by a system of equations on A. In this note we give a semantic characterization for algebraic functions on quasiprimal algebras. This characterization is applied to obtain necessary and sufficient conditions for a quasiprimal algebra A to have every one of its algebraic functions be a term function. We also apply our results to particular algebras such as finite fields and monadic algebras.