"商集合" meaning in 日本語

See 商集合 in All languages combined, or Wiktionary

Noun

  1. ある同値関係を使って集合を同値類に分けたときの、存在しうる全ての同値類から成る集合。同値類系ともいう。
    Sense id: ja-商集合-ja-noun-1hNZuULD Categories (other): 日本語 代数学, 日本語 集合論 Topics: algebra, set theory
The following are not (yet) sense-disambiguated
Related terms: 類別, 代表元, 完全代表系
Categories (other): 日本語, 日本語_名詞
{
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      "source": "w"
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      "parents": [],
      "source": "w"
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  ],
  "lang": "日本語",
  "lang_code": "ja",
  "notes": [
    "集合を A とし、同値関係を ∼ で表すとき、 ∼ を使って A を分けて得られる商集合を A/∼ と表す。"
  ],
  "pos": "noun",
  "pos_title": "名詞",
  "related": [
    {
      "word": "類別"
    },
    {
      "word": "代表元"
    },
    {
      "word": "完全代表系"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "日本語 代数学",
          "parents": [],
          "source": "w"
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        {
          "kind": "other",
          "name": "日本語 集合論",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "ある同値関係を使って集合を同値類に分けたときの、存在しうる全ての同値類から成る集合。同値類系ともいう。"
      ],
      "id": "ja-商集合-ja-noun-1hNZuULD",
      "topics": [
        "algebra",
        "set theory"
      ]
    }
  ],
  "word": "商集合"
}
{
  "categories": [
    "日本語",
    "日本語_名詞"
  ],
  "lang": "日本語",
  "lang_code": "ja",
  "notes": [
    "集合を A とし、同値関係を ∼ で表すとき、 ∼ を使って A を分けて得られる商集合を A/∼ と表す。"
  ],
  "pos": "noun",
  "pos_title": "名詞",
  "related": [
    {
      "word": "類別"
    },
    {
      "word": "代表元"
    },
    {
      "word": "完全代表系"
    }
  ],
  "senses": [
    {
      "categories": [
        "日本語 代数学",
        "日本語 集合論"
      ],
      "glosses": [
        "ある同値関係を使って集合を同値類に分けたときの、存在しうる全ての同値類から成る集合。同値類系ともいう。"
      ],
      "topics": [
        "algebra",
        "set theory"
      ]
    }
  ],
  "word": "商集合"
}

Download raw JSONL data for 商集合 meaning in 日本語 (0.7kB)


This page is a part of the kaikki.org machine-readable 日本語 dictionary. This dictionary is based on structured data extracted on 2025-07-19 from the jawiktionary dump dated 2025-07-02 using wiktextract (45c4a21 and f1c2b61). 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.