There seem to be two conflicting definitions for *p-adic valuation* in the literature.

Firstly, for any non-zero integer n, we have $\nu=\nu_p(n)$ is the greatest non-negative integer such that $p^\nu$ divides $n$. Secondly, we have $|n|_p$ which is defined as $1/p^\nu$. [These definitions can be extended to the rationals.]

$\nu$ is defined as the p-adic valuation in Khrennikov, Nilson, *P-adic deterministic and random dynamics* (for example) and $|\cdot|_p$ is defined as the p-adic valuation in Khrennikov, *P-adic and group valued probabilities*, in Harmonic, wavelet and p-adic analysis (for example).

Question: Is there a preferred definition for p-adic valuation?

multiplicative valuationand the other theadditive valuation. – Robin Chapman Nov 7 '10 at 9:23Algebraan absolute value is a valuation if it satisifes $|x + y| \leqq \max(|x|, |y|)$. – Dylan Moreland Nov 7 '10 at 18:31