See p-adic on Wiktionary
Download JSON data for p-adic meaning in All languages combined (4.0kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "p",
"3": "adic"
},
"expansion": "p + -adic",
"name": "suffix"
},
{
"args": {
"1": "en",
"2": "p"
},
"expansion": "p",
"name": "m"
},
{
"args": {
"1": "en",
"2": "-adic"
},
"expansion": "-adic",
"name": "m"
}
],
"etymology_text": "From p + -adic. The letter p follows common number theory usage in representing an arbitrary prime number; the suffix -adic signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.",
"head_templates": [
{
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"1": "-",
"head": "p-adic"
},
"expansion": "p-adic (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms containing italics",
"parents": [
"Terms containing italics",
"Terms by orthographic property",
"Terms by lexical property"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms suffixed with -adic",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "p-adic absolute value"
},
{
"word": "p-adic norm"
},
{
"word": "p-adic number"
},
{
"word": "p-adic order"
},
{
"word": "p-adic ordinal"
},
{
"word": "p-adic ultrametric"
}
],
"examples": [
{
"ref": "1995, Alain Escassut, Analytic Elements in P-adic Analysis, World Scientific, page v",
"text": "The theory of p-adic analytic functions in domains other than simple disks is not very well known yet, although such kind of functions happens to intervene in questions linked to p-adic functional analysis, number theory, and others.",
"type": "quotation"
},
{
"text": "1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60,\nDefinition 3.3.3 The ring of p'''-adic integers is the valuation ring\nZ ₚ=x∈ Q ₚ:|x|ₚ<1."
},
{
"ref": "2007, Nguyen Minh Cheung, Nguyen Van Co, Le Quang Thuan, §12: Harmonic Analysis Over P-adic Field I: Some Equations and Singular Field Operators, N. M. Chuong, Yu V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (editors), Harmonic, Wavelet and P-adic Analysis, World Scientific, page 272, The paper is organized as follows",
"text": "2. Preliminaries\n3. A p'''-adic Cauchy problem\n4. The p'''-adic Hilbert transform\n5. The boundaries in the p'''-adic space L^q\n[…]"
}
],
"glosses": [
"Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"id": "en-p-adic-en-adj-k3jWjy7j",
"links": [
[
"number theory",
"number theory"
],
[
"p-adic number",
"p-adic number"
]
],
"raw_glosses": [
"(number theory) Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"related": [
{
"word": "ℓ-adic cohomology"
},
{
"word": "p-adic Riemann zeta function"
}
],
"synonyms": [
{
"sense": "of, etc., p-adic numbers",
"word": "ℓ-adic"
}
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "Translations",
"word": "p-àdic"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "p-adinen"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"word": "p-adique"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"word": "p-adisch"
},
{
"code": "it",
"lang": "Italian",
"sense": "Translations",
"word": "p-adico"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"word": "p-adyczny"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "Translations",
"word": "p-ádico"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Translations",
"word": "p-adic"
},
{
"code": "es",
"lang": "Spanish",
"sense": "Translations",
"word": "p-ádico"
}
],
"wikipedia": [
"Weil cohomology theory"
]
}
],
"word": "p-adic"
}
{
"derived": [
{
"word": "p-adic absolute value"
},
{
"word": "p-adic norm"
},
{
"word": "p-adic number"
},
{
"word": "p-adic order"
},
{
"word": "p-adic ordinal"
},
{
"word": "p-adic ultrametric"
}
],
"etymology_templates": [
{
"args": {
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"2": "p",
"3": "adic"
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{
"args": {
"1": "en",
"2": "p"
},
"expansion": "p",
"name": "m"
},
{
"args": {
"1": "en",
"2": "-adic"
},
"expansion": "-adic",
"name": "m"
}
],
"etymology_text": "From p + -adic. The letter p follows common number theory usage in representing an arbitrary prime number; the suffix -adic signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.",
"head_templates": [
{
"args": {
"1": "-",
"head": "p-adic"
},
"expansion": "p-adic (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"word": "ℓ-adic cohomology"
},
{
"word": "p-adic Riemann zeta function"
}
],
"senses": [
{
"categories": [
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"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English terms containing italics",
"English terms suffixed with -adic",
"English terms with quotations",
"English uncomparable adjectives",
"Translation table header lacks gloss",
"en:Number theory"
],
"examples": [
{
"ref": "1995, Alain Escassut, Analytic Elements in P-adic Analysis, World Scientific, page v",
"text": "The theory of p-adic analytic functions in domains other than simple disks is not very well known yet, although such kind of functions happens to intervene in questions linked to p-adic functional analysis, number theory, and others.",
"type": "quotation"
},
{
"text": "1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60,\nDefinition 3.3.3 The ring of p'''-adic integers is the valuation ring\nZ ₚ=x∈ Q ₚ:|x|ₚ<1."
},
{
"ref": "2007, Nguyen Minh Cheung, Nguyen Van Co, Le Quang Thuan, §12: Harmonic Analysis Over P-adic Field I: Some Equations and Singular Field Operators, N. M. Chuong, Yu V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (editors), Harmonic, Wavelet and P-adic Analysis, World Scientific, page 272, The paper is organized as follows",
"text": "2. Preliminaries\n3. A p'''-adic Cauchy problem\n4. The p'''-adic Hilbert transform\n5. The boundaries in the p'''-adic space L^q\n[…]"
}
],
"glosses": [
"Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"links": [
[
"number theory",
"number theory"
],
[
"p-adic number",
"p-adic number"
]
],
"raw_glosses": [
"(number theory) Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"Weil cohomology theory"
]
}
],
"synonyms": [
{
"sense": "of, etc., p-adic numbers",
"word": "ℓ-adic"
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "Translations",
"word": "p-àdic"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "p-adinen"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"word": "p-adique"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"word": "p-adisch"
},
{
"code": "it",
"lang": "Italian",
"sense": "Translations",
"word": "p-adico"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"word": "p-adyczny"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "Translations",
"word": "p-ádico"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Translations",
"word": "p-adic"
},
{
"code": "es",
"lang": "Spanish",
"sense": "Translations",
"word": "p-ádico"
}
],
"word": "p-adic"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-09 from the enwiktionary dump dated 2024-05-02 using wiktextract (4d5d0bb and edd475d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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