Abstract Algebra: Theory and Applications

What does it mean for an extension field $E$ of a field $F$ to be a simple extension of $F\text{?}$

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 $F\text{?}$

Describe how linear algebra enters into this chapter. What critical result relies on a proof that is almost entirely linear algebra?

What is the definition of an algebraically closed field?

What is a splitting field of a polynomial $p(x)\in F[x]\text{?}$