p-adic norm

短语

词形变化

p-adic norms 复数 p-adic norms

释义与例句

n.
  1. 1.

    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).

    数学

    2002, M. Ram Murty, Introduction to p-adic Analytic Number Theory, American Mathematical Society, page 114, By the property of the p'''-adic norm, (or by the “isosceles triangle principle”) we deduce that operatorname ordₚa_r=rλ₁.

    2006, Matti Pitkanen, Topological Geometrodynamics, Luniver Press, page 531, The definition of p-adic norm should obey the usual conditions, in particular the requirement that the norm of product is product of norms.

  2. 2.

    A norm on a vector space which is defined over a field equipped with a discrete valuation (a generalisation of p-adic absolute value).

    数学