"abelian group" meaning in 英語

{
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    {
      "kind": "other",
      "name": "有1個詞條的頁面",
      "parents": [],
      "source": "w"
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      "name": "有詞條的頁面",
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    {
      "kind": "other",
      "name": "英語可數名詞",
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    {
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    {
      "kind": "other",
      "name": "英語詞元",
      "parents": [],
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    }
  ],
  "derived": [
    {
      "word": "free abelian group"
    }
  ],
  "etymology_text": "以挪威數學家尼爾斯·亨利克·阿貝爾（1802–1829）的名字命名。",
  "forms": [
    {
      "form": "abelian groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "hypernyms": [
    {
      "word": "group"
    },
    {
      "word": "solvable group"
    }
  ],
  "hyponyms": [
    {
      "word": "cyclic group"
    },
    {
      "word": "free abelian group"
    },
    {
      "word": "torsion subgroup"
    }
  ],
  "lang": "英語",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "名詞",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "有引文的英語詞",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "英語 代數",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1986年，Partially Ordered Abelian Groups with Interpolation，美國數學學會，2010年平裝再版，第12頁,",
          "text": "Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group"
        },
        {
          "ref": "2000年，David Arnold，Abelian Groups and Representations of Finite Partially Ordered Sets，Springer，第1版平裝再版，第74頁,",
          "text": "Chapter 2 is a brief introduction to some fundamental techniques for countable torsion-free abelian groups."
        },
        {
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          ],
          "ref": "2013，Karl H. Hofmann, Sidney A. Morris，The Structure of Compact Groups: A Primer for the Student: A Handbook for the Expert，Walter de Gruyter，頁 299:",
          "text": "By the end of Chapter 2 we had the full power of the Pontryagin Duality Theorem for compact abelian groups and for discrete abelian groups. Locally compact abelian groups are much closer to compact abelian groups than is apparent at first sight.",
          "translation": "到第2章結束時，我們已經掌握了緊緻阿貝爾群和離散阿貝爾群的龐特里亞金對偶定理的全部力量。局部緊緻阿貝爾群與緊緻阿貝爾群的相似性比乍看之下更為接近。"
        }
      ],
      "glosses": [
        "阿貝爾群，交換群"
      ],
      "id": "zh-abelian_group-en-noun-egQljg05",
      "raw_tags": [
        "代數"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/əˈbi.li.ən ɡɹup/"
    },
    {
      "ipa": "/əˈbil.jən ɡɹup/"
    }
  ],
  "synonyms": [
    {
      "word": "Abelian group"
    },
    {
      "sense": "阿貝爾群，交換群",
      "word": "commutative group"
    }
  ],
  "word": "abelian group"
}

{
  "categories": [
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    "英語名詞",
    "英語詞元"
  ],
  "derived": [
    {
      "word": "free abelian group"
    }
  ],
  "etymology_text": "以挪威數學家尼爾斯·亨利克·阿貝爾（1802–1829）的名字命名。",
  "forms": [
    {
      "form": "abelian groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "hypernyms": [
    {
      "word": "group"
    },
    {
      "word": "solvable group"
    }
  ],
  "hyponyms": [
    {
      "word": "cyclic group"
    },
    {
      "word": "free abelian group"
    },
    {
      "word": "torsion subgroup"
    }
  ],
  "lang": "英語",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "名詞",
  "senses": [
    {
      "categories": [
        "有引文的英語詞",
        "英語 代數"
      ],
      "examples": [
        {
          "ref": "1986年，Partially Ordered Abelian Groups with Interpolation，美國數學學會，2010年平裝再版，第12頁,",
          "text": "Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group"
        },
        {
          "ref": "2000年，David Arnold，Abelian Groups and Representations of Finite Partially Ordered Sets，Springer，第1版平裝再版，第74頁,",
          "text": "Chapter 2 is a brief introduction to some fundamental techniques for countable torsion-free abelian groups."
        },
        {
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            [
              92,
              106
            ],
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            ],
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            ],
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            ]
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            ]
          ],
          "ref": "2013，Karl H. Hofmann, Sidney A. Morris，The Structure of Compact Groups: A Primer for the Student: A Handbook for the Expert，Walter de Gruyter，頁 299:",
          "text": "By the end of Chapter 2 we had the full power of the Pontryagin Duality Theorem for compact abelian groups and for discrete abelian groups. Locally compact abelian groups are much closer to compact abelian groups than is apparent at first sight.",
          "translation": "到第2章結束時，我們已經掌握了緊緻阿貝爾群和離散阿貝爾群的龐特里亞金對偶定理的全部力量。局部緊緻阿貝爾群與緊緻阿貝爾群的相似性比乍看之下更為接近。"
        }
      ],
      "glosses": [
        "阿貝爾群，交換群"
      ],
      "raw_tags": [
        "代數"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/əˈbi.li.ən ɡɹup/"
    },
    {
      "ipa": "/əˈbil.jən ɡɹup/"
    }
  ],
  "synonyms": [
    {
      "word": "Abelian group"
    },
    {
      "sense": "阿貝爾群，交換群",
      "word": "commutative group"
    }
  ],
  "word": "abelian group"
}