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Nick
Posts:
18
Registered:
4/12/08


Field extension  dimension splitting field.
Posted:
Jul 18, 2013 5:32 AM


An exercise in a book (Galois Theory, Ian Stewart) asks for the splitting field of polynomial t^6  8 over the Rationals and the degree of this splitting field.
The book answer is that the splitting field is Q(2^(1/2), e^(i*pi/3)) and that its degree is 12.
Now I think the splitting field given in the book is ok but that its degree is 4 not 12.
My preferred representation of the splitting field extension would be Q(2^(1/2), i * 3^(1/2)).
Unfortunately the book is from 1982 and there doesn't appear to be published errata for this edition on the web.
I'm pretty sure I'm right but would like to check.



