Field Extensions

Abstract

Field extensions F < E can be characterized in a variety of useful ways. Some characterizations involve properties of the individual elements of the extension. For instance, an extension F < E is algebraic if each element α ∈ E is algebraic over F. Other characterizations involve the field E as a whole. For instance, F < E is normal if E is the splitting field for a family of polynomials over F. In this chapter, we will describe several types of extensions and study their basic properties.