page1921 Rings Matthias Lorentzen...mattegrisenforlag.com
Look at the picture beneath, then
scroll down to the question and click the correct Answer button.
Question
Consider the field extension `QQ(e^10)` of `QQ`,
where e is the base of the natural logarithm.
Which of the following statements is true?
A) The polynomial `p(x) = x^5 - e^10` is reducible over `QQ(e^10)`,
and `e^2` is an element of `QQ(e^10)`.
B) The polynomial `p(x) = x^5 - e^10` is irreducible over `QQ(e^10)`,
and `e^2` is algebraic of degree 5 over `QQ(e^10)`
?
