Discrete Valuation

A discrete valuation on a field is a nontrivial function such that exactly when , , and . It is normalized if . The associated valuation ring is $O_v={x:v(x)>=0}$ , and its unique maximal ideal is $m_v={x:v(x)>0}$ .

See also

Additive Valuation, Discrete Valuation Ring, Local Field, Maximal Ideal, Valuation, Valuation Ring

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References

Serre, J.-P. Local Fields. New York: Springer-Verlag, 1979.

Cite this as:

Weisstein, Eric W. "Discrete Valuation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DiscreteValuation.html

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