Talk:Absolute value (algebra)

Naming convention

Such a function is known as a valuation. Some authors call it an exponential valuation, and call what Wikipedia calls an absolute value a valuation; Wikipedia is following the terminology of Bourbaki.

Wikipedia should not refer to itself by name. I don't know exactly what's trying to be said here, or I'd fix it myself.

18.251.5.233 08:14, 27 February 2007 (UTC)

Attempted to reword it. Awyong J. M. Salleh 08:33, 27 February 2007 (UTC)

Prime places

does anyone think we should change "main article:prime place" to link to Algebraic_number_field#Archimedean_places rather than Prime_place since the latter is an orphan, and the first reference is more detailed and readable as well as covering the same ground? —Preceding unsigned comment added by 128.250.30.165 (talk) 04:14, 21 December 2009 (UTC)

Trivial absolute values

I'd like to add a little more information to the bit about trivial absolute values. Maybe something like this:

Every integral domain has at least one absolute value, called the trivial value. This is the absolute value with | x | = 0 when x = 0 and | x | = 1 otherwise. The trivial value is the only possible value on a finite field.

Thoughts? Vectornaut (talk) 18:37, 24 August 2011 (UTC)

Looks like you did that, and no one complained. 67.198.37.16 (talk) 01:13, 6 October 2020 (UTC)

Unclear sentence

I removed the sentence Ultrametric complete fields are far more numerous, however. as it did not appear to mean anything. Is there a source that can explain this? Deltahedron (talk) 06:24, 23 August 2012 (UTC)

What's unclear? There are fields, with an ultrametric, that can be completed. Don't know what makes them numerous, perhaps something to do with the transcendence degree of a function field or an algebraic function field or something like that. Ok, so that's indeed unclear. 67.198.37.16 (talk) 01:18, 6 October 2020 (UTC)

Incorrect definition

The definition of valuation may be wrong. I think it should be |x+y| \geq max{|x|,|y|}, not min. — Preceding unsigned comment added by 71.182.184.12 (talk) 16:47, 11 June 2015 (UTC)

Looks like it has been fixed already. 67.198.37.16 (talk) 01:20, 6 October 2020 (UTC)

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Relationship between absolute values and norm is unclear

The introduction says that "'norm' usually refers to a specific kind of absolute value on a field," but norms are defined on vector fields where multiplication of two vectors is not (in general) defined, so the multiplicativity property of absolute values is not valid. Can we clarify the relationship beween absolute values and norms? It seems to me that the set of absolute value functions are a subset of norm functions and not vice versa. The-erinaceous-one (talk) 23:58, 9 September 2020 (UTC)