See noetherian on Wiktionary
{
"derived": [
{
"_dis1": "0 0 0 0 0 0",
"word": "noetherian module"
}
],
"etymology_text": "From Emmy Noether.",
"forms": [
{
"form": "Noetherian",
"tags": [
"alternative"
]
}
],
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "noetherian (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"_dis1": "0 0 0 0 0 0",
"word": "Artinian"
},
{
"_dis1": "0 0 0 0 0 0",
"word": "ascending chain condition"
}
],
"senses": [
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [],
"source": "w"
},
{
"_dis": "22 22 22 21 5 9",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 23 23 22 4 5",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 22 22 21 6 7",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 24 24 24 1 2",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Basque translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 23 3 4",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 22 22 22 4 7",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "18 18 18 17 16 14",
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of ideals eventually becomes constant."
],
"id": "en-noetherian-en-adj-en:ring",
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"ring",
"ring"
],
[
"ideal",
"ideal"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a ring) In which any ascending chain of ideals eventually becomes constant."
],
"raw_tags": [
"of a ring"
],
"senseid": [
"en:ring"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [],
"source": "w"
},
{
"_dis": "22 22 22 21 5 9",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 23 23 22 4 5",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 22 22 21 6 7",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 24 24 24 1 2",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Basque translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 23 3 4",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 22 22 22 4 7",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "18 18 18 17 16 14",
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of submodules eventually becomes constant."
],
"id": "en-noetherian-en-adj-YHa-pN3q",
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"module",
"module"
],
[
"submodule",
"submodule"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a module) In which any ascending chain of submodules eventually becomes constant."
],
"raw_tags": [
"of a module"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [],
"source": "w"
},
{
"_dis": "22 22 22 21 5 9",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 23 23 22 4 5",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 22 22 21 6 7",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 24 24 24 1 2",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Basque translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 23 3 4",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 22 22 22 4 7",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "18 18 18 17 16 14",
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of subgroups eventually becomes constant."
],
"id": "en-noetherian-en-adj-x4nTr~TI",
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"group",
"group"
],
[
"subgroup",
"subgroup"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a group) In which any ascending chain of subgroups eventually becomes constant."
],
"raw_tags": [
"of a group"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [],
"source": "w"
},
{
"_dis": "22 22 22 21 5 9",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 23 23 22 4 5",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "21 22 22 21 6 7",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 24 24 24 1 2",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Basque translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 23 3 4",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "24 23 23 22 4 4",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "23 22 22 22 4 7",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "18 18 18 17 16 14",
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of open subsets eventually becomes constant."
],
"id": "en-noetherian-en-adj-ix2a6oIy",
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"topological space",
"topological space"
],
[
"open",
"open"
],
[
"subset",
"subset"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a topological space) In which any ascending chain of open subsets eventually becomes constant."
],
"raw_tags": [
"of a topological space"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "18 18 18 17 16 14",
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Such that the converse relation is well-founded (on that set)."
],
"id": "en-noetherian-en-adj-eHjZcbdC",
"links": [
[
"mathematics",
"mathematics"
],
[
"binary relation",
"binary relation"
],
[
"set",
"set"
],
[
"converse relation",
"converse relation"
],
[
"well-founded",
"well-founded"
]
],
"raw_glosses": [
"(mathematics, of a binary relation on a set) Such that the converse relation is well-founded (on that set)."
],
"raw_tags": [
"of a binary relation on a set"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Algebraic geometry",
"orig": "en:Algebraic geometry",
"parents": [],
"source": "w"
},
{
"_dis": "18 18 18 17 16 14",
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;"
],
"id": "en-noetherian-en-adj-1-1QGC84",
"links": [
[
"algebraic geometry",
"algebraic geometry"
],
[
"scheme",
"scheme"
],
[
"admitting",
"admit"
],
[
"finite",
"finite"
],
[
"affine",
"affine"
],
[
"noetherian ring",
"noetherian#English:_ring"
]
],
"raw_glosses": [
"(algebraic geometry, of a scheme) admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;"
],
"raw_tags": [
"of a scheme"
],
"tags": [
"not-comparable"
],
"topics": [
"algebraic-geometry",
"geometry",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/noʊˈθɪəriən/"
},
{
"audio": "LL-Q1860 (eng)-Flame, not lame-noetherian.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/76/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/76/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav.ogg"
}
],
"translations": [
{
"_dis1": "18 18 18 18 13 16",
"code": "eu",
"lang": "Basque",
"sense": "math",
"word": "noetherdar"
},
{
"_dis1": "18 18 18 18 13 16",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "math",
"word": "诺特的"
},
{
"_dis1": "18 18 18 18 13 16",
"code": "fr",
"lang": "French",
"sense": "math",
"word": "noethérien"
},
{
"_dis1": "18 18 18 18 13 16",
"code": "it",
"lang": "Italian",
"sense": "math",
"word": "noetheriano"
}
],
"word": "noetherian"
}
{
"categories": [
"English 3-syllable words",
"English adjectives",
"English entries with incorrect language header",
"English eponyms",
"English lemmas",
"English terms with IPA pronunciation",
"English uncomparable adjectives",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Basque translations",
"Terms with French translations",
"Terms with Italian translations",
"Terms with Mandarin translations",
"en:Mathematics"
],
"derived": [
{
"word": "noetherian module"
}
],
"etymology_text": "From Emmy Noether.",
"forms": [
{
"form": "Noetherian",
"tags": [
"alternative"
]
}
],
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "noetherian (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"word": "Artinian"
},
{
"word": "ascending chain condition"
}
],
"senses": [
{
"categories": [
"en:Algebra"
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of ideals eventually becomes constant."
],
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"ring",
"ring"
],
[
"ideal",
"ideal"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a ring) In which any ascending chain of ideals eventually becomes constant."
],
"raw_tags": [
"of a ring"
],
"senseid": [
"en:ring"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Algebra"
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of submodules eventually becomes constant."
],
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"module",
"module"
],
[
"submodule",
"submodule"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a module) In which any ascending chain of submodules eventually becomes constant."
],
"raw_tags": [
"of a module"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Algebra"
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of subgroups eventually becomes constant."
],
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"group",
"group"
],
[
"subgroup",
"subgroup"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a group) In which any ascending chain of subgroups eventually becomes constant."
],
"raw_tags": [
"of a group"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Algebra"
],
"glosses": [
"Satisfying some (usually ascending) chain condition:",
"In which any ascending chain of open subsets eventually becomes constant."
],
"links": [
[
"algebra",
"algebra"
],
[
"ascending",
"ascending"
],
[
"topological space",
"topological space"
],
[
"open",
"open"
],
[
"subset",
"subset"
]
],
"raw_glosses": [
"(algebra) Satisfying some (usually ascending) chain condition:",
"(of a topological space) In which any ascending chain of open subsets eventually becomes constant."
],
"raw_tags": [
"of a topological space"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Mathematics"
],
"glosses": [
"Such that the converse relation is well-founded (on that set)."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"binary relation",
"binary relation"
],
[
"set",
"set"
],
[
"converse relation",
"converse relation"
],
[
"well-founded",
"well-founded"
]
],
"raw_glosses": [
"(mathematics, of a binary relation on a set) Such that the converse relation is well-founded (on that set)."
],
"raw_tags": [
"of a binary relation on a set"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Algebraic geometry"
],
"glosses": [
"admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;"
],
"links": [
[
"algebraic geometry",
"algebraic geometry"
],
[
"scheme",
"scheme"
],
[
"admitting",
"admit"
],
[
"finite",
"finite"
],
[
"affine",
"affine"
],
[
"noetherian ring",
"noetherian#English:_ring"
]
],
"raw_glosses": [
"(algebraic geometry, of a scheme) admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;"
],
"raw_tags": [
"of a scheme"
],
"tags": [
"not-comparable"
],
"topics": [
"algebraic-geometry",
"geometry",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/noʊˈθɪəriən/"
},
{
"audio": "LL-Q1860 (eng)-Flame, not lame-noetherian.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/76/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/7/76/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-noetherian.wav.ogg"
}
],
"translations": [
{
"code": "eu",
"lang": "Basque",
"sense": "math",
"word": "noetherdar"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "math",
"word": "诺特的"
},
{
"code": "fr",
"lang": "French",
"sense": "math",
"word": "noethérien"
},
{
"code": "it",
"lang": "Italian",
"sense": "math",
"word": "noetheriano"
}
],
"word": "noetherian"
}
Download raw JSONL data for noetherian meaning in All languages combined (5.1kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-13 from the enwiktionary dump dated 2025-05-01 using wiktextract (9a214a4 and 1b6da77). 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.