ABSTRACT
As indicated in the introduction to Part II, some of the most beautiful re sults of algebra involve polynomials. Upon first acquaintance, a polynomial seems rather ethereal - a formal expression involving an indeterminate x and coefficients from a given ring R - and one might expect that we must substitute some value for x in order to obtain meaningful results. However, it turns out that the collection of all these polynomials can be given the structure of a ring having many nice properties which are inherited from R , and in this sublime transition from chaos to algebraic structure, x becomes a very meaningful element of the new ring.
