See division ring on Wiktionary
Download JSON data for division ring meaning in All languages combined (3.0kB)
{
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"expansion": "division ring (plural division rings)",
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"glosses": [
"A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = xa = 1."
],
"hypernyms": [
{
"word": "noncommutative ring"
}
],
"hyponyms": [
{
"word": "division algebra"
},
{
"word": "field"
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],
"id": "en-division_ring-en-noun-CNVuB6xY",
"links": [
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"(algebra) A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = xa = 1."
],
"synonyms": [
{
"word": "skew field"
}
],
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"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "algebraic concept",
"tags": [
"neuter"
],
"word": "těleso"
},
{
"code": "nl",
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"sense": "algebraic concept",
"tags": [
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"word": "scheef lichaam"
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{
"code": "fi",
"lang": "Finnish",
"sense": "algebraic concept",
"word": "jakorengas"
},
{
"code": "fr",
"lang": "French",
"sense": "algebraic concept",
"tags": [
"masculine"
],
"word": "anneau à division"
},
{
"code": "fr",
"lang": "French",
"sense": "algebraic concept",
"tags": [
"masculine"
],
"word": "corps gauche"
},
{
"code": "fr",
"lang": "French",
"sense": "algebraic concept",
"tags": [
"masculine"
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"word": "corps non commutatif"
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{
"code": "fr",
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"sense": "algebraic concept",
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"word": "corps"
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{
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"masculine"
],
"word": "pierścień z dzieleniem"
},
{
"code": "pl",
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"sense": "algebraic concept",
"tags": [
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"word": "ciało nieprzemienne"
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],
"wikipedia": [
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"word": "division ring"
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"glosses": [
"A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = xa = 1."
],
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"algebra",
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],
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"(algebra) A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = xa = 1."
],
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"sciences"
],
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"synonyms": [
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"translations": [
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"code": "cs",
"lang": "Czech",
"sense": "algebraic concept",
"tags": [
"neuter"
],
"word": "těleso"
},
{
"code": "nl",
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{
"code": "nl",
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"word": "scheef lichaam"
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{
"code": "fi",
"lang": "Finnish",
"sense": "algebraic concept",
"word": "jakorengas"
},
{
"code": "fr",
"lang": "French",
"sense": "algebraic concept",
"tags": [
"masculine"
],
"word": "anneau à division"
},
{
"code": "fr",
"lang": "French",
"sense": "algebraic concept",
"tags": [
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"word": "corps gauche"
},
{
"code": "fr",
"lang": "French",
"sense": "algebraic concept",
"tags": [
"masculine"
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"word": "corps non commutatif"
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{
"code": "fr",
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"word": "corps"
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{
"code": "pl",
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"sense": "algebraic concept",
"tags": [
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"word": "pierścień z dzieleniem"
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{
"code": "pl",
"lang": "Polish",
"sense": "algebraic concept",
"tags": [
"dated",
"neuter"
],
"word": "ciało nieprzemienne"
}
],
"word": "division ring"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). 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.