See algebraic number theory on Wiktionary
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "algebraic number",
"3": "number theory"
},
"expansion": "Blend of algebraic number + number theory",
"name": "blend"
}
],
"etymology_text": "Blend of algebraic number + number theory. Possibly (alternatively or also) a calque of German algebraische Zahlentheorie.",
"head_templates": [
{
"args": {
"1": "-",
"head": "algebraic number theory"
},
"expansion": "algebraic number theory (uncountable)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English blends",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Mandarin terms with redundant transliterations",
"parents": [
"Terms with redundant transliterations",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Armenian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "1998, Norbert Klingen, Arithmetical Similarities: Prime Decomposition and Finite Group Theory, Oxford University Press (Clarendon Press), page 241:",
"text": "As is well-known in algebraic number theory, there is a far-reaching analogy between number fields and algebraic function fields in one variable with finite constant field.",
"type": "quote"
},
{
"ref": "2008, Steven H. Weintraub, Factorization: Unique and Otherwise, CRC Press, page 143:",
"text": "The field of mathematics that these generalize to is known as algebraic number theory. As a matter of historical fact, our development here parallels the development of algebraic number theory.",
"type": "quote"
},
{
"ref": "2013, Mak Trifković, Algebraic Theory of Quadratic Numbers, Springer, page v:",
"text": "Elementary arithmetic studies divisibility and factorization of ordinary integers, Algebraic number theory considers the same questions for algebraic numbers, solutions to polynomial equations with integer coefficients. In this setting, (un)fortunately, the uniqueness of prime factorization no longer holds. Remedying and measuring its failure is the starting point of algebraic number theory.",
"type": "quote"
}
],
"glosses": [
"The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra."
],
"id": "en-algebraic_number_theory-en-noun-hPffYqNK",
"links": [
[
"mathematics",
"mathematics"
],
[
"number theory",
"number theory"
],
[
"algebraic number field",
"algebraic number field"
],
[
"algebra",
"algebra"
]
],
"raw_glosses": [
"(mathematics, number theory) The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra."
],
"related": [
{
"word": "analytic number theory"
},
{
"word": "arithmetic geometry"
},
{
"word": "diophantine geometry"
}
],
"tags": [
"uncountable"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "hanrahašvakan tʻveri tesutʻyun",
"sense": "branch of number theory concerning algebraic number fields",
"word": "հանրահաշվական թվերի տեսություն"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "branch of number theory concerning algebraic number fields",
"word": "代數數論"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "dàishùshùlùn",
"sense": "branch of number theory concerning algebraic number fields",
"word": "代数数论"
},
{
"code": "de",
"lang": "German",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "algebraische Zahlentheorie"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria algebrica dei numeri"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria dei numeri algebrica"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria dos números algébricos"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria algébrica dos números"
}
],
"wikipedia": [
"algebraic number theory"
]
}
],
"word": "algebraic number theory"
}
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "algebraic number",
"3": "number theory"
},
"expansion": "Blend of algebraic number + number theory",
"name": "blend"
}
],
"etymology_text": "Blend of algebraic number + number theory. Possibly (alternatively or also) a calque of German algebraische Zahlentheorie.",
"head_templates": [
{
"args": {
"1": "-",
"head": "algebraic number theory"
},
"expansion": "algebraic number theory (uncountable)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "analytic number theory"
},
{
"word": "arithmetic geometry"
},
{
"word": "diophantine geometry"
}
],
"senses": [
{
"categories": [
"English blends",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"English uncountable nouns",
"Entries with translation boxes",
"Mandarin terms with redundant transliterations",
"Pages with 1 entry",
"Pages with entries",
"Terms with Armenian translations",
"Terms with German translations",
"Terms with Italian translations",
"Terms with Mandarin translations",
"Terms with Portuguese translations",
"en:Mathematics",
"en:Number theory"
],
"examples": [
{
"ref": "1998, Norbert Klingen, Arithmetical Similarities: Prime Decomposition and Finite Group Theory, Oxford University Press (Clarendon Press), page 241:",
"text": "As is well-known in algebraic number theory, there is a far-reaching analogy between number fields and algebraic function fields in one variable with finite constant field.",
"type": "quote"
},
{
"ref": "2008, Steven H. Weintraub, Factorization: Unique and Otherwise, CRC Press, page 143:",
"text": "The field of mathematics that these generalize to is known as algebraic number theory. As a matter of historical fact, our development here parallels the development of algebraic number theory.",
"type": "quote"
},
{
"ref": "2013, Mak Trifković, Algebraic Theory of Quadratic Numbers, Springer, page v:",
"text": "Elementary arithmetic studies divisibility and factorization of ordinary integers, Algebraic number theory considers the same questions for algebraic numbers, solutions to polynomial equations with integer coefficients. In this setting, (un)fortunately, the uniqueness of prime factorization no longer holds. Remedying and measuring its failure is the starting point of algebraic number theory.",
"type": "quote"
}
],
"glosses": [
"The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"number theory",
"number theory"
],
[
"algebraic number field",
"algebraic number field"
],
[
"algebra",
"algebra"
]
],
"raw_glosses": [
"(mathematics, number theory) The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra."
],
"tags": [
"uncountable"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"algebraic number theory"
]
}
],
"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "hanrahašvakan tʻveri tesutʻyun",
"sense": "branch of number theory concerning algebraic number fields",
"word": "հանրահաշվական թվերի տեսություն"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "branch of number theory concerning algebraic number fields",
"word": "代數數論"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "dàishùshùlùn",
"sense": "branch of number theory concerning algebraic number fields",
"word": "代数数论"
},
{
"code": "de",
"lang": "German",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "algebraische Zahlentheorie"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria algebrica dei numeri"
},
{
"code": "it",
"lang": "Italian",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria dei numeri algebrica"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria dos números algébricos"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "branch of number theory concerning algebraic number fields",
"tags": [
"feminine"
],
"word": "teoria algébrica dos números"
}
],
"word": "algebraic number theory"
}
Download raw JSONL data for algebraic number theory meaning in All languages combined (4.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.