Talk:Field norm
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what about the definition, norm on F is map from F to R satisfying:
1) N(a) = 0 iff a = 0 2) N(ab) = N(a)N(b) 3) triangle inequality
this is also called a "field norm" in some contexts. Revolver 12:19, 10 Nov 2004 (UTC)
Well, I don't think the terminology is very standard either way; but isn't that is more a valuation? Charles Matthews 12:34, 10 Nov 2004 (UTC)
- Yes, you're right. I've been reading Koblitz the past few weeks, and he uses the term "field norm" for "valuation", so that's probably why I thought this, but yes, valuation is more standard. Revolver 13:35, 10 Nov 2004 (UTC)
- No, sorry, doesn't use "field norm" for "valuation", not sure he uses anything for valuation. But I have seen "absolute value" or "valued field" for what you would call what you get from a valuation into the positive reals under multiplication, except the "ultra" part isn't required, (if that makes sense). Revolver 13:51, 10 Nov 2004 (UTC)
What we really need is a good treatment of topological field, then ...
Charles Matthews 17:32, 10 Nov 2004 (UTC)