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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2015 • Question 9

Question

Math 6310 • Algebra Fall 2015 • Question 9

Let \(E\) be the splitting field of \(f(x)=x^{14}+1\) over \(\mathbb {F}_2\), and let \(K\) be the splitting field \(g(x)=x^{21}+1\) over \(\mathbb {F}_2\). Prove that \(K\) contains an isomorphic copy of \(E\), and compute the extension degree of \(K\) over \(E\).

Raw LaTeX

Let \(E\) be the splitting field of \(f(x)=x^{14}+1\) over \(\mathbb{F}_2\), and let \(K\) be the
splitting field \(g(x)=x^{21}+1\) over \(\mathbb{F}_2\). Prove that \(K\) contains an isomorphic copy
of \(E\), and compute the extension degree of \(K\) over \(E\).

Topic Tags

Ext Functors and Module Extensions Field Extensions Finite Fields Splitting Fields