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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Summer 2021 • Question 1

Question

Math 6320 • Algebra II Summer 2021 • Question 1

Determine whether the following two fields \(K\) and \(L\) are isomorphic; if they are isomorphic then construct an explicit isomorphism between them.

\[ K = \mathbb {Q}[x]/(x^2+2x+2),\quad L = \mathbb {Q}(i) \subset \mathbb {C}. \]

Raw LaTeX

Determine whether the following two fields \(K\) and \(L\) are isomorphic; if they are isomorphic then construct an
explicit isomorphism between them.

\[
K = \mathbb{Q}[x]/(x^2+2x+2),\quad L = \mathbb{Q}(i) \subset \mathbb{C}.
\]

Topic Tags

Field Extensions