Field theory and polynomials Valued and topological fields Concept
Valuation
Summary
A valuation on a field measures how divisible an element is, with values in a totally ordered abelian group, see the definition. The value of a product is the sum of the values. The value of a sum is at least the smaller of the two values. The p-adic valuation on the rationals is the model case. Valuations give valuation rings, non-Archimedean absolute values and the whole theory of valued fields.
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| Tag | B85T5VKR3M |
|---|---|
| URI | m2://B85T5VKR3M |
| Kind | concept |
| Writing | W0 stub |
| MSC | 12J20, 13F30 |
| Same as | |
| Changed | 2 November 2026 |
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