Noun
(number theory) A p-adic absolute value, for a given prime number p, the function, denoted |..|p and defined on the rational numbers, such that |0|p = 0 and, for x≠0, |x|p = p, where ordp(x) is the p-adic ordinal of x; the same function, extended to the p-adic numbers ℚp (the completion of the rational numbers with respect to the p-adic ultrametric defined by said absolute value); the same function, further extended to some extension of ℚp (for example, its algebraic closure).
(algebra) A norm on a vector space which is defined over a field equipped with a discrete valuation (a generalisation of p-adic absolute value).
Source: en.wiktionary.org