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Ypsilon IV

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I feel pretty comfortable when representing norms as determinants of linear operators but I seem to be stuck with representing norms as product of isomorphims.

I have read Lang's GTM Algebra, but I really would like to see an example, how it works.

I would really appreciate if someone could help me with the guidelines how to find the norm for say Q(sqrt(2), sqrt(3)). Thanks in advance!