Tuesday, 21 March 2017

abstract algebra - mathbbQ(zetam)capmathbbQ(zetan)=mathbbQ(zetad)



Prove that Q(ζm)Q(ζn)=Q(ζd) where d=gcd(m,n).




I want to solve this problem without Galois theory.



I know only about field extension. For example, algebraic extension, cyclotomic extension, splitting field and algebraic closure.



Can I solve it without Galois theory?

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