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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2015 • Question 10

Question

Math 6310 • Algebra Spring 2015 • Question 10

Let \(K\) be a field of characteristic \(p>0\), and let \(t\) be an indeterminate. Consider the automorphism \(\sigma \in \operatorname {Aut}_K K(t)\) with \(\sigma (t)=t+1\). Determine the subfield of \(K(t)\) that is fixed by \(\sigma \).

Raw LaTeX

Let \(K\) be a field of characteristic \(p>0\), and let \(t\) be an indeterminate. Consider the
automorphism \(\sigma\in\operatorname{Aut}_K K(t)\) with \(\sigma(t)=t+1\). Determine the
subfield of \(K(t)\) that is fixed by \(\sigma\).

Topic Tags

Field Extensions