Introduction

Abstract

In this book we shall assume that the reader is familiar with the general notions of algebra and the results on fields which appear in Vol. I, and with the more elementary parts of Vol. II. In particular, we presuppose a knowledge of the characteristic of a field, prime field, construction of the field of fractions of a commutative integral domain, construction of simple algebraic and transcendental extensions of a field. These ideas appear in Chaps. II and III of Vol. I. We shall need also the elementary factorization theory of Chap. IV. From Vol. II we require the basic notions of vector space over a field, dimensionality, linear transformation, linear function, compositions of linear transformations, bilinear form. On the other hand, the deeper results on canonical forms of linear transformations and bilinear forms will not be needed.