##  [P-Adic Valuation](/p-adic-valuation) 

  ##  [P-Adic Valuation](https://mathlogic.quantumdictionary.io/p-adic-valuation-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function v_p that assigns to each nonzero integer n the exponent of a fixed prime p dividing n; extended to rationals by v_p(a/b)=v_p(a)−v_p(b) and further to fields and valuation rings to measure p-adic divisibility and induce the p-adic absolute value.