"division ring" meaning in All languages combined

See division ring on Wiktionary

Noun [English]

Forms: division rings [plural]
Head templates: {{en-noun}} division ring (plural division rings)
  1. (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. Wikipedia link: division ring Categories (topical): Algebra, Ring theory Synonyms: skew field Hypernyms: noncommutative ring Hyponyms: division algebra, field Translations (algebraic concept): těleso [neuter] (Czech), lichaam [Belgium, neuter] (Dutch), scheef lichaam [Netherlands, neuter] (Dutch), jakorengas (Finnish), anneau à division [masculine] (French), corps gauche [masculine] (French), corps non commutatif [masculine] (French), corps [masculine] (French), pierścień z dzieleniem [masculine] (Polish), ciało nieprzemienne [dated, neuter] (Polish)

Inflected forms

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    {
      "form": "division rings",
      "tags": [
        "plural"
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  "lang_code": "en",
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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"
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          "word": "field"
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      "id": "en-division_ring-en-noun-CNVuB6xY",
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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"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
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      "translations": [
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          "code": "cs",
          "lang": "Czech",
          "sense": "algebraic concept",
          "tags": [
            "neuter"
          ],
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          "code": "nl",
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          "code": "nl",
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            "Netherlands",
            "neuter"
          ],
          "word": "scheef lichaam"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "algebraic concept",
          "word": "jakorengas"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "algebraic concept",
          "tags": [
            "masculine"
          ],
          "word": "anneau à division"
        },
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          "code": "fr",
          "lang": "French",
          "sense": "algebraic concept",
          "tags": [
            "masculine"
          ],
          "word": "corps gauche"
        },
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          "code": "fr",
          "lang": "French",
          "sense": "algebraic concept",
          "tags": [
            "masculine"
          ],
          "word": "corps non commutatif"
        },
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          "code": "fr",
          "lang": "French",
          "sense": "algebraic concept",
          "tags": [
            "masculine"
          ],
          "word": "corps"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "algebraic concept",
          "tags": [
            "masculine"
          ],
          "word": "pierścień z dzieleniem"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "algebraic concept",
          "tags": [
            "dated",
            "neuter"
          ],
          "word": "ciało nieprzemienne"
        }
      ],
      "wikipedia": [
        "division ring"
      ]
    }
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  "word": "division ring"
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    }
  ],
  "hyponyms": [
    {
      "word": "division algebra"
    },
    {
      "word": "field"
    }
  ],
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  "lang_code": "en",
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      ],
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      ],
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        "sciences"
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      ]
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  "synonyms": [
    {
      "word": "skew field"
    }
  ],
  "translations": [
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "algebraic concept",
      "tags": [
        "neuter"
      ],
      "word": "těleso"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "algebraic concept",
      "tags": [
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      ],
      "word": "lichaam"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "algebraic concept",
      "tags": [
        "Netherlands",
        "neuter"
      ],
      "word": "scheef lichaam"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "algebraic concept",
      "word": "jakorengas"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "algebraic concept",
      "tags": [
        "masculine"
      ],
      "word": "anneau à division"
    },
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      "code": "fr",
      "lang": "French",
      "sense": "algebraic concept",
      "tags": [
        "masculine"
      ],
      "word": "corps gauche"
    },
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      "code": "fr",
      "lang": "French",
      "sense": "algebraic concept",
      "tags": [
        "masculine"
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      "word": "corps non commutatif"
    },
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      "code": "fr",
      "lang": "French",
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      ],
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    },
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      "code": "pl",
      "lang": "Polish",
      "sense": "algebraic concept",
      "tags": [
        "masculine"
      ],
      "word": "pierścień z dzieleniem"
    },
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      "code": "pl",
      "lang": "Polish",
      "sense": "algebraic concept",
      "tags": [
        "dated",
        "neuter"
      ],
      "word": "ciało nieprzemienne"
    }
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  "word": "division ring"
}

Download raw JSONL data for division ring meaning in All languages combined (2.4kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.