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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2013 • Question 10

Question

Math 6310 • Algebra Fall 2013 • Question 10

Explain (preferably in a sentence!) why \(\mathbb {F}_3[x]/(x^2-2)\) and \(\mathbb {F}_3[x]/(x^2-2x-1)\) are isomorphic. Then construct an explicit isomorphism.

Raw LaTeX

Explain (preferably in a sentence!) why
\(\mathbb{F}_3[x]/(x^2-2)\) and \(\mathbb{F}_3[x]/(x^2-2x-1)\) are isomorphic. Then construct an
explicit isomorphism.

Topic Tags

Finite Fields Ideals and Quotient Rings