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Reading Questions 21.4 Reading Questions
1. 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
\(p(x)\in F[x]\text{?}\)
