ABSTRACT
In many digital signal processing applications, one is required to process data sequences defined over a given number system. This number system may either be a field or a ring of finite or infinite order. In this chapter, we present some fundamental results in the theory of polynomial algebra for polynomials defined over a field. We observe here that all the results valid for polynomials defined over infinite fields are also valid for polynomials defined over finite fields. The order of the field does not play a very critical role in the fundamental characterization of polynomial algebra. The important distinction to be drawn is between the polynomials defined over fields and rings. Many basic results in polynomial algebra over a field are not valid for polynomial algebra over a ring.
