See p-adic norm in All languages combined, or Wiktionary
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"text": "2002, M. Ram Murty, Introduction to p-adic Analytic Number Theory, American Mathematical Society, page 114,\nBy the property of the p'''-adic norm, (or by the “isosceles triangle principle”) we deduce that operatorname ordₚa_r=rλ₁."
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"text": "2006, Matti Pitkanen, Topological Geometrodynamics, Luniver Press, page 531,\nThe definition of p-adic norm should obey the usual conditions, in particular the requirement that the norm of product is product of norms."
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"ref": "2012, Claire C. Ralph, Santiago R. Simanca, Arithmetic Differential Operators over the p-adic Integers, Cambridge University Press, page 2:",
"text": "Given a prime p, we may define the p'''-adic norm #x5C;Vert#x5C;#x5C;Vert#x5F;p over the field of rational numbers #x5C;Q.",
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"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)."
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"(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^(-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)."
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