Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $F = \mathbb{Q}(\pi^3)$. How can we find a basis for $F(\pi)$ over $F$ ?

share|improve this question
    
let me know if another hint is needed –  Belgi Dec 4 '12 at 10:56

1 Answer 1

up vote 6 down vote accepted

Well, as a good hint I'd say that $\,\pi\,$ is a root of $\,f(x):=x^3-\pi^3\in\Bbb Q(\pi^3)[x]=:\Bbb F[x]\,$ , and from here $\,[\Bbb F(\pi):\Bbb F]\leq 3\,$...

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.