Chapter 3 Field Fundamentals 3 . 1 Field Extensions

    If F is a field and F [X] is the set of all polynomials over F, that is, polynomials with coefficients in F , we know that F [X] is a Euclidean domain, and therefore a principal ideal domain and a unique factorization domain (see Sections 2.6 and 2.7). Thus any nonzero polynomial f in F [X] can be factored uniquely as a product of irreducible polynomials… (More)