A **discrete valuation** is a special type of valuation defined on a field, which gives a way to measure the "size" of elements in that field. More specifically, a discrete valuation provides a way to assess how "close" elements are to zero in a field, often in the context of algebraic number theory or local fields.
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A discrete valuation on a field is a surjective group homomorphism satisfying whenever . Its valuation ring is .