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Topic: Field extension - dimension splitting field.
Replies: 6   Last Post: Jul 18, 2013 11:42 AM

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Posts: 50
Registered: 4/12/08
Field extension - dimension splitting field.
Posted: Jul 18, 2013 5:32 AM
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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.

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