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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Summer 2022 • Question 5

Question

Math 6320 • Algebra II Summer 2022 • Question 5

Let \(L\) be the splitting field of \((x^3+2x+1)(x^3+x^2+2)(x^2+1)\) over \(\mathbb {F}_3\). How many proper subfields does \(L\) have?

Raw LaTeX

Let \(L\) be the splitting field of
\((x^3+2x+1)(x^3+x^2+2)(x^2+1)\) over \(\mathbb{F}_3\). How many proper
subfields does \(L\) have?

Topic Tags

Finite Fields Splitting Fields