The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: about the Kronecker-Weber theorem
Replies: 6   Last Post: Feb 4, 2013 7:45 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 12,067
Registered: 7/15/05
Re: about the Kronecker-Weber theorem
Posted: Feb 4, 2013 4:04 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

David Bernier wrote:
>I have a further question about conjugate roots ...
>The non-trivial third roots of unity
>-1/2 +i*srqrt(3)/2 and -1/2 -i*srqrt(3)/2
>are complex conjugates.
>I don't know of a definition where, for example, in the
>setting above,
>2^(1/3) is said to be conjugate to
>2^(1/3) * (-1/2 +i*srqrt(3)/2).

Let H be an algebraically closed field, and let K be a
subfield of H. Let K[x] denote the ring of all polynomials
in the indeterminate x with coefficients in K. If f in K[x]
is irreducible in K[x], the roots of f in H are said to be
conjugates of each other over K.

Thus, the 3 cube roots of 2 are conjugate over Q since
they are roots of the polynomial x^3 - 2 which is irreducible
over Q.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.