Skip to main content
Contents Index Dark Mode Prev Up Next \(\newcommand{\identity}{\mathrm{id}}
\newcommand{\notdivide}{\nmid}
\newcommand{\notsubset}{\not\subset}
\newcommand{\lcm}{\operatorname{lcm}}
\newcommand{\gf}{\operatorname{GF}}
\newcommand{\inn}{\operatorname{Inn}}
\newcommand{\aut}{\operatorname{Aut}}
\newcommand{\Hom}{\operatorname{Hom}}
\newcommand{\cis}{\operatorname{cis}}
\newcommand{\chr}{\operatorname{char}}
\newcommand{\Null}{\operatorname{Null}}
\newcommand{\transpose}{\text{t}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
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
\(p(x)\in F[x]\text{?}\)
