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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2013 • Question 9

Question

Math 6310 • Algebra Fall 2013 • Question 9

Let \(\zeta \) be a primitive 16-th root of unity over a field \(K\). Determine \([K(\zeta ):K]\) when \(K\) is:

  1. \(\mathbb {F}_7\)
  2. \(\mathbb {F}_9\)
  3. \(\mathbb {F}_{17}\)

Raw LaTeX

Let \(\zeta\) be a primitive 16-th root of unity over a field \(K\). Determine \([K(\zeta):K]\) when
\(K\) is:
\begin{enumerate}
\item
\(\mathbb{F}_7\)

\item
\(\mathbb{F}_9\)

\item
\(\mathbb{F}_{17}\)
\end{enumerate}

Topic Tags

Cyclotomic Fields Finite Fields