p-adic norm (English, noun)
expansion: p-adic norm (plural p-adic norms)
Senses:
topics: mathematics
number-theory
sciences
glosses: 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^(-ordₚ(x)), 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).
topics: algebra
mathematics
sciences
glosses: A norm on a vector space which is defined over a field equipped with a discrete valuation (a generalisation of p-adic absolute value).
Forms:
form: p-adic norms
tags: plural