ABSTRACT
A technique which has become very useful in mathematics is that of associating with a given structure a different one, of a type better understood. In this chapter we exploit the technique by associating with any field extension a vector space. This places at our disposal the machinery of linear algebra-a very successful algebraic theory-and with its aid we can make considerable progress. The machinery is sufficiently powerful to solve three notorious problems which remained unanswered for over two thousand years. We shall discuss these problems in the next chapter, and devote the present chapter to developing the theory.
