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p-adic absolute value

p-adic absolute value noun: a norm for the rational numbers, with some prime number p as parameter, such that any rational number of the form pᵏ(a/b) — where a, b and k are integers and a, b and p are coprime — is mapped to the rational number p⁻ᵏ and 0 is mapped to 0. (Note: any nonzero rational number can be reduced to such a form.).

Noun

p-adic absolute value (plural p-adic absolute values)

  1. (field theory) A norm for the rational numbers, with some prime number p as parameter, such that any rational number of the form pᵏ(a/b) — where a, b and k are integers and a, b and p are coprime — is mapped to the rational number p⁻ᵏ and 0 is mapped to 0. (Note: any nonzero rational number can be reduced to such a form.)
    • According to Ostrowski's theorem, only three kinds of norms are possible for the set of real numbers: the trivial absolute value, the real absolute value, and the p-adic absolute value.ᵂᴾ
    • If cgt;1, then x#92;rightarrowc#123;-v#95;p(x)#125; (with the convention c#123;-#92;infty#125;#61;0) is a nonarchimedean absolute value, denoted #92;vert..#92;vert#95;#123;p,c#125; and called the p-adic absolute value to base c. If cgt;1 and dgt;1 and if r#61;#92;log#95;cd, then...1993, Seth Warner, Topological Rings, Elsevier (North-Holland), page 8
    Synonyms:
    p-adic norm

Synonyms of p-adic absolute value

Forms of p-adic absolute value

pluralp-adic absolute values

Questions about p-adic absolute value

What does p-adic absolute value mean?
P-adic absolute value means a norm for the rational numbers, with some prime number p as parameter, such that any rational number of the form pᵏ(a/b) — where a, b and k are integers and a, b and p are coprime — is mapped to the rational number p⁻ᵏ and 0 is mapped to 0. (Note: any nonzero rational number can be reduced to such a form.).
What part of speech is p-adic absolute value?
P-adic absolute value is a noun.
What is the plural of p-adic absolute value?
The plural of p-adic absolute value is p-adic absolute values.

Words near p-adic absolute value in the dictionary

  1. P-1As
  2. P-A
  3. P-A conduction time
  4. p-acetylaminophenol
  5. p-adic
  6. p-adic absolute value
  7. p-adic absolute values
  8. p-adic norm
  9. p-adic norms
  10. p-adic number
  11. p-adic numbers

Source and license

Adapted from Wiktionary: p-adic absolute value (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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