Talk:Ideal norm
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Field and Ideal norms are different[edit]
Norm of an element and norm of an ideal are different. The definition of norm of an ideal given in field norm is wrong (or not complete). Please be careful and considerate before removing a newly made article. Make sure you discuss the future removals of the article here in the talk page. OmerKs 22:43, 8 April 2007 (UTC)
What is S ???[edit]
The initial part of this article includes the passage:
"The norm of an ideal I of S is defined as follows",
but there is no other reference to S -- it is not defined. This should be fixed.Daqu (talk) 21:41, 11 June 2008 (UTC)
- My fault… awhile back I changed the notation to be more standard, and missed that S ! Should be fixed now. GromXXVII (talk) 00:53, 12 June 2008 (UTC)
Norm of an element bounded by...[edit]
Counterexample: If L is the rationals, then this says |N(x)| is at most N(alpha). But let alpha be 2Z, and let x be 4. In fact, given a nontorsion element of O_L, we can multiply x by this element as many times as we like, increasing the norm of x the whole time while remaining in the ideal alpha. Is this inequality backwards? —Preceding unsigned comment added by 188.220.224.110 (talk) 17:33, 9 December 2010 (UTC)
Definition[edit]
I'm not particular happy with the definition given here. For one, I don't think you need any "Galois" assumption. Also, the discussion should distinguish local and global situations (or so I understand :). Anyway, I simply will go ahead and rewrite the article. I hope I'm not too bold. -- Taku (talk) 20:25, 16 August 2011 (UTC)