"nilpotent" meaning in English

See nilpotent in All languages combined, or Wiktionary

Adjective

IPA: /nɪlˈpəʊtənt/ Audio: LL-Q1860 (eng)-Flame, not lame-nilpotent.wav
Etymology: From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras. Etymology templates: {{compound|en|nil|potent|t1=not any|t2=having power}} nil (“not any”) + potent (“having power”), {{uder|en|la|-}} Latin Head templates: {{en-adj|-}} nilpotent (not comparable)
  1. (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0. Tags: not-comparable Categories (topical): Algebra, Mathematics
    Sense id: en-nilpotent-en-adj-uY-zS2oB Topics: algebra, mathematics, sciences
  2. (mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
    (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
    Tags: not-comparable Categories (topical): Algebra, Mathematics
    Sense id: en-nilpotent-en-adj-2TRXtgrX Categories (other): English entries with incorrect language header, English undefined derivations, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Czech translations, Terms with Danish translations, Terms with Esperanto translations, Terms with Finnish translations, Terms with French translations, Terms with Russian translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 6 15 10 9 24 9 22 4 Disambiguation of English undefined derivations: 6 16 11 9 21 9 20 7 Disambiguation of Entries with translation boxes: 4 23 13 11 18 11 17 2 Disambiguation of Pages with 1 entry: 7 15 11 10 21 10 21 7 Disambiguation of Pages with entries: 7 17 12 8 25 8 23 2 Disambiguation of Terms with Czech translations: 6 18 13 11 18 11 18 4 Disambiguation of Terms with Danish translations: 5 27 13 9 17 9 18 2 Disambiguation of Terms with Esperanto translations: 5 21 12 9 21 9 21 3 Disambiguation of Terms with Finnish translations: 5 21 13 10 19 10 18 3 Disambiguation of Terms with French translations: 5 22 13 9 20 9 19 3 Disambiguation of Terms with Russian translations: 5 24 12 8 20 8 20 3 Disambiguation of Terms with Spanish translations: 5 22 13 8 21 8 21 2 Topics: algebra, mathematics, sciences
  3. (mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
    (Lie theory, of a Lie algebra) Such that the lower central series terminates.
    Tags: not-comparable Categories (topical): Algebra, Mathematics
    Sense id: en-nilpotent-en-adj-pJCI5500 Categories (other): English entries with incorrect language header, English undefined derivations, Pages with 1 entry, Pages with entries, Terms with Czech translations, Terms with Esperanto translations, Terms with Finnish translations, Terms with French translations, Terms with Russian translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 6 15 10 9 24 9 22 4 Disambiguation of English undefined derivations: 6 16 11 9 21 9 20 7 Disambiguation of Pages with 1 entry: 7 15 11 10 21 10 21 7 Disambiguation of Pages with entries: 7 17 12 8 25 8 23 2 Disambiguation of Terms with Czech translations: 6 18 13 11 18 11 18 4 Disambiguation of Terms with Esperanto translations: 5 21 12 9 21 9 21 3 Disambiguation of Terms with Finnish translations: 5 21 13 10 19 10 18 3 Disambiguation of Terms with French translations: 5 22 13 9 20 9 19 3 Disambiguation of Terms with Russian translations: 5 24 12 8 20 8 20 3 Disambiguation of Terms with Spanish translations: 5 22 13 8 21 8 21 2 Topics: algebra, mathematics, sciences
  4. (mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
    (group theory, of a group) Admitting a central series of finite length.
    Tags: not-comparable Categories (topical): Algebra, Group theory, Mathematics
    Sense id: en-nilpotent-en-adj-dcFIXuSL Categories (other): Terms with Czech translations, Terms with Finnish translations Disambiguation of Terms with Czech translations: 6 18 13 11 18 11 18 4 Disambiguation of Terms with Finnish translations: 5 21 13 10 19 10 18 3 Topics: algebra, group-theory, mathematics, sciences
  5. (mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
    (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
    Tags: not-comparable Categories (topical): Algebra, Mathematics
    Sense id: en-nilpotent-en-adj-AePFLvz~ Categories (other): English entries with incorrect language header, English undefined derivations, Pages with 1 entry, Pages with entries, Terms with Czech translations, Terms with Esperanto translations, Terms with Finnish translations, Terms with French translations, Terms with Russian translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 6 15 10 9 24 9 22 4 Disambiguation of English undefined derivations: 6 16 11 9 21 9 20 7 Disambiguation of Pages with 1 entry: 7 15 11 10 21 10 21 7 Disambiguation of Pages with entries: 7 17 12 8 25 8 23 2 Disambiguation of Terms with Czech translations: 6 18 13 11 18 11 18 4 Disambiguation of Terms with Esperanto translations: 5 21 12 9 21 9 21 3 Disambiguation of Terms with Finnish translations: 5 21 13 10 19 10 18 3 Disambiguation of Terms with French translations: 5 22 13 9 20 9 19 3 Disambiguation of Terms with Russian translations: 5 24 12 8 20 8 20 3 Disambiguation of Terms with Spanish translations: 5 22 13 8 21 8 21 2 Topics: algebra, mathematics, sciences
  6. (mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
    (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
    Tags: not-comparable Categories (topical): Algebra, Mathematics
    Sense id: en-nilpotent-en-adj-t3WM7HnH Categories (other): Terms with Czech translations, Terms with Finnish translations Disambiguation of Terms with Czech translations: 6 18 13 11 18 11 18 4 Disambiguation of Terms with Finnish translations: 5 21 13 10 19 10 18 3 Topics: algebra, mathematics, sciences
  7. (mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
    (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
    Tags: not-comparable Categories (topical): Algebra, Mathematics
    Sense id: en-nilpotent-en-adj-YO81Fm0w Categories (other): English entries with incorrect language header, English undefined derivations, Pages with 1 entry, Pages with entries, Terms with Czech translations, Terms with Esperanto translations, Terms with Finnish translations, Terms with French translations, Terms with Russian translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 6 15 10 9 24 9 22 4 Disambiguation of English undefined derivations: 6 16 11 9 21 9 20 7 Disambiguation of Pages with 1 entry: 7 15 11 10 21 10 21 7 Disambiguation of Pages with entries: 7 17 12 8 25 8 23 2 Disambiguation of Terms with Czech translations: 6 18 13 11 18 11 18 4 Disambiguation of Terms with Esperanto translations: 5 21 12 9 21 9 21 3 Disambiguation of Terms with Finnish translations: 5 21 13 10 19 10 18 3 Disambiguation of Terms with French translations: 5 22 13 9 20 9 19 3 Disambiguation of Terms with Russian translations: 5 24 12 8 20 8 20 3 Disambiguation of Terms with Spanish translations: 5 22 13 8 21 8 21 2 Topics: algebra, mathematics, sciences
The following are not (yet) sense-disambiguated
Derived forms: nilpotent algebra, nilpotent ideal, nilpotently, nilpotent orbit, nilpotent semigroup Related terms: nilpotence, nilpotency, idempotent, nullipotent, unipotent Coordinate_terms: idempotent Translations ((algebra)): nilpotentní (Czech), nilpotent (Danish), nilpotenta (Esperanto), nulpotenca (Esperanto), nilpotentti (Finnish), nilpotent (French), нильпотент (nilʹpotent) (Russian), nilpotente (Spanish)
Disambiguation of '(algebra)': 7 15 15 15 15 15 15

Noun

IPA: /nɪlˈpəʊtənt/ Audio: LL-Q1860 (eng)-Flame, not lame-nilpotent.wav Forms: nilpotents [plural]
Etymology: From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras. Etymology templates: {{compound|en|nil|potent|t1=not any|t2=having power}} nil (“not any”) + potent (“having power”), {{uder|en|la|-}} Latin Head templates: {{en-noun}} nilpotent (plural nilpotents)
  1. (algebra) A nilpotent element. Categories (topical): Algebra
    Sense id: en-nilpotent-en-noun-noEHS11f Topics: algebra, mathematics, sciences

Inflected forms

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      "categories": [
        "en:Algebra",
        "en:Mathematics"
      ],
      "glosses": [
        "In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.",
        "Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ],
        [
          "commutative",
          "commutative"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "index",
          "index"
        ]
      ],
      "raw_glosses": [
        "(mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.",
        "(of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero."
      ],
      "raw_tags": [
        "of an algebra over a commutative ring"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/nɪlˈpəʊtənt/"
    },
    {
      "audio": "LL-Q1860 (eng)-Flame, not lame-nilpotent.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav.ogg"
    }
  ],
  "translations": [
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "(algebra)",
      "word": "nilpotentní"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "(algebra)",
      "word": "nilpotent"
    },
    {
      "code": "eo",
      "lang": "Esperanto",
      "sense": "(algebra)",
      "word": "nilpotenta"
    },
    {
      "code": "eo",
      "lang": "Esperanto",
      "sense": "(algebra)",
      "word": "nulpotenca"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "(algebra)",
      "word": "nilpotentti"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "(algebra)",
      "word": "nilpotent"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "nilʹpotent",
      "sense": "(algebra)",
      "word": "нильпотент"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "(algebra)",
      "word": "nilpotente"
    }
  ],
  "wikipedia": [
    "Benjamin Peirce",
    "nilpotent"
  ],
  "word": "nilpotent"
}

{
  "categories": [
    "English adjectives",
    "English compound terms",
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English nouns",
    "English terms derived from Latin",
    "English uncomparable adjectives",
    "English undefined derivations",
    "Entries with translation boxes",
    "Pages with 1 entry",
    "Pages with entries",
    "Terms with Czech translations",
    "Terms with Danish translations",
    "Terms with Esperanto translations",
    "Terms with Finnish translations",
    "Terms with French translations",
    "Terms with Russian translations",
    "Terms with Spanish translations"
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "nil",
        "3": "potent",
        "t1": "not any",
        "t2": "having power"
      },
      "expansion": "nil (“not any”) + potent (“having power”)",
      "name": "compound"
    },
    {
      "args": {
        "1": "en",
        "2": "la",
        "3": "-"
      },
      "expansion": "Latin",
      "name": "uder"
    }
  ],
  "etymology_text": "From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens.\nCoined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.",
  "forms": [
    {
      "form": "nilpotents",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "nilpotent (plural nilpotents)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Algebra"
      ],
      "examples": [
        {
          "ref": "2015, Garret Sobczyk, “Part I: Vector Analysis of Spinors”, in 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.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A nilpotent element."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ]
      ],
      "raw_glosses": [
        "(algebra) A nilpotent element."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/nɪlˈpəʊtənt/"
    },
    {
      "audio": "LL-Q1860 (eng)-Flame, not lame-nilpotent.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-nilpotent.wav.ogg"
    }
  ],
  "wikipedia": [
    "Benjamin Peirce",
    "nilpotent"
  ],
  "word": "nilpotent"
}

Download raw JSONL data for nilpotent meaning in English (12.6kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.