What does it mean for an extension field \(E\) of a field \(F\) to be a simple extension of \(F\text{?}\)
2.
What is the definition of a minimal polynomial of an element \(\alpha\in E\text{,}\) where \(E\) is an extension of \(F\text{,}\) and \(\alpha\) is algebraic over \(F\text{?}\)
3.
Describe how linear algebra enters into this chapter. What critical result relies on a proof that is almost entirely linear algebra?
4.
What is the definition of an algebraically closed field?
5.
What is a splitting field of a polynomial \(p(x)\in F[x]\text{?}\)
