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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1999 • Question 9

Question

Math 6310 • Algebra Fall 1999 • Question 9

Let \(K\) be an arbitrary field, and let \(L\) be an extension of \(K\) obtained by adjoining a root of the polynomial \(X^n-1\) for some integer \(n\ge 1\). Show that \(L\) is Galois over \(K\) with abelian Galois group.

Raw LaTeX

Let \(K\) be an arbitrary field, and let \(L\) be an extension of \(K\) obtained by adjoining a root of
the polynomial \(X^n-1\) for some integer \(n\ge 1\). Show that \(L\) is Galois over \(K\) with abelian
Galois group.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Field Extensions Galois Groups of Polynomials Galois Theory