
Chapter 6
The Degree of an Extension
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 suf-
ficiently 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 ...