page1923 Rings Matthias Lorentzen...mattegrisenforlag.com
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Question
Consider the field extension ℚ of QQ,
where e is the base of the natural logarithm.
Which of the following statements is true?
A) p(x) is reducible over Q(e^10) because
e^2 is a root of p(x) and Q(e^10) contains
all rational functions of e^10.
B) p(x) is irreducible over Q(e^10) because
e^2, e^4, e^6, and e^8 are not elements of Q(e^10),
despite e^2 being a root of p(x).
?
