"nilpotent" meaning in 英語

{
  "categories": [
    {
      "kind": "other",
      "name": "派生自拉丁語的英語詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語形容詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語無比較級形容詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語複合詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語詞元",
      "parents": [],
      "source": "w"
    }
  ],
  "derived": [
    {
      "word": "nilpotent algebra"
    },
    {
      "word": "nilpotent ideal"
    },
    {
      "word": "nilpotently"
    },
    {
      "word": "nilpotent orbit"
    },
    {
      "word": "nilpotent semigroup"
    }
  ],
  "etymology_text": "來自nil (“沒有任何”) + potent (“有冪”)，字面意義即「有零冪次」。兩個字根分別來自拉丁語 nil 和 potens。由美國數學家本傑明·皮爾斯（Benjamin Peirce）於1870年與idempotent一起創造，使用於結合代數等領域。",
  "lang": "英語",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "word": "idempotent"
    },
    {
      "word": "nilpotence"
    },
    {
      "word": "nilpotency"
    },
    {
      "word": "idempotent"
    },
    {
      "word": "nullipotent"
    },
    {
      "word": "unipotent"
    }
  ],
  "senses": [
    {
      "examples": [
        {
          "ref": "2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129,",
          "text": "The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements."
        }
      ],
      "glosses": [
        "冪零的"
      ],
      "id": "zh-nilpotent-en-adj-E5jHZvhB",
      "raw_tags": [
        "代數",
        "環論",
        "半群或環之元素 x 的"
      ]
    }
  ],
  "tags": [
    "not-comparable"
  ],
  "translations": [
    {
      "lang": "捷克語",
      "lang_code": "cs",
      "sense": "冪零的",
      "word": "nilpotentní"
    },
    {
      "lang": "丹麥語",
      "lang_code": "da",
      "sense": "冪零的",
      "word": "nilpotent"
    },
    {
      "lang": "芬蘭語",
      "lang_code": "fi",
      "sense": "冪零的",
      "word": "nilpotentti"
    },
    {
      "lang": "俄語",
      "lang_code": "ru",
      "sense": "冪零的",
      "word": "нильпотент"
    }
  ],
  "word": "nilpotent"
}

{
  "categories": [
    {
      "kind": "other",
      "name": "英語可數名詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語名詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語詞元",
      "parents": [],
      "source": "w"
    }
  ],
  "etymology_text": "來自nil (“沒有任何”) + potent (“有冪”)，字面意義即「有零冪次」。兩個字根分別來自拉丁語 nil 和 potens。由美國數學家本傑明·皮爾斯（Benjamin Peirce）於1870年與idempotent一起創造，使用於結合代數等領域。",
  "forms": [
    {
      "form": "nilpotents",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "英語",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "examples": [
        {
          "ref": "2015, Garret Sobczyk, “Part I: Vector Analysis of Spinors”, 出自 arXiv:",
          "text": "The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle."
        }
      ],
      "glosses": [
        "冪零元、冪零元素"
      ],
      "id": "zh-nilpotent-en-noun-nbl3TvS4",
      "raw_tags": [
        "代數"
      ]
    }
  ],
  "word": "nilpotent"
}

{
  "categories": [
    "派生自拉丁語的英語詞",
    "英語形容詞",
    "英語無比較級形容詞",
    "英語複合詞",
    "英語詞元"
  ],
  "derived": [
    {
      "word": "nilpotent algebra"
    },
    {
      "word": "nilpotent ideal"
    },
    {
      "word": "nilpotently"
    },
    {
      "word": "nilpotent orbit"
    },
    {
      "word": "nilpotent semigroup"
    }
  ],
  "etymology_text": "來自nil (“沒有任何”) + potent (“有冪”)，字面意義即「有零冪次」。兩個字根分別來自拉丁語 nil 和 potens。由美國數學家本傑明·皮爾斯（Benjamin Peirce）於1870年與idempotent一起創造，使用於結合代數等領域。",
  "lang": "英語",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "word": "idempotent"
    },
    {
      "word": "nilpotence"
    },
    {
      "word": "nilpotency"
    },
    {
      "word": "idempotent"
    },
    {
      "word": "nullipotent"
    },
    {
      "word": "unipotent"
    }
  ],
  "senses": [
    {
      "examples": [
        {
          "ref": "2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129,",
          "text": "The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements."
        }
      ],
      "glosses": [
        "冪零的"
      ],
      "raw_tags": [
        "代數",
        "環論",
        "半群或環之元素 x 的"
      ]
    }
  ],
  "tags": [
    "not-comparable"
  ],
  "translations": [
    {
      "lang": "捷克語",
      "lang_code": "cs",
      "sense": "冪零的",
      "word": "nilpotentní"
    },
    {
      "lang": "丹麥語",
      "lang_code": "da",
      "sense": "冪零的",
      "word": "nilpotent"
    },
    {
      "lang": "芬蘭語",
      "lang_code": "fi",
      "sense": "冪零的",
      "word": "nilpotentti"
    },
    {
      "lang": "俄語",
      "lang_code": "ru",
      "sense": "冪零的",
      "word": "нильпотент"
    }
  ],
  "word": "nilpotent"
}

{
  "categories": [
    "英語可數名詞",
    "英語名詞",
    "英語詞元"
  ],
  "etymology_text": "來自nil (“沒有任何”) + potent (“有冪”)，字面意義即「有零冪次」。兩個字根分別來自拉丁語 nil 和 potens。由美國數學家本傑明·皮爾斯（Benjamin Peirce）於1870年與idempotent一起創造，使用於結合代數等領域。",
  "forms": [
    {
      "form": "nilpotents",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "英語",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "examples": [
        {
          "ref": "2015, Garret Sobczyk, “Part I: Vector Analysis of Spinors”, 出自 arXiv:",
          "text": "The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle."
        }
      ],
      "glosses": [
        "冪零元、冪零元素"
      ],
      "raw_tags": [
        "代數"
      ]
    }
  ],
  "word": "nilpotent"
}