"semisimple" meaning in All languages combined

See semisimple on Wiktionary

Adjective [English]

Etymology: From semi- + simple. Etymology templates: {{prefix|en|semi|simple}} semi- + simple Head templates: {{en-adj|-}} semisimple (not comparable)
  1. (mathematics, of a module) In which each submodule is a direct summand. Tags: not-comparable Categories (topical): Mathematics
    Sense id: en-semisimple-en-adj-P-xK9P2i Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 2 entries Disambiguation of English entries with incorrect language header: 12 21 10 29 28 Disambiguation of English terms prefixed with semi-: 27 23 14 19 16 Disambiguation of Pages with 2 entries: 15 28 9 31 17 Topics: mathematics, sciences
  2. (mathematics, of an algebra or ring) diagonalizable. Tags: not-comparable Categories (topical): Mathematics
    Sense id: en-semisimple-en-adj--0w7RsfT Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 2 entries Disambiguation of English entries with incorrect language header: 12 21 10 29 28 Disambiguation of English terms prefixed with semi-: 27 23 14 19 16 Disambiguation of Pages with 2 entries: 15 28 9 31 17 Topics: mathematics, sciences
  3. (mathematics, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree. Tags: not-comparable Categories (topical): Mathematics
    Sense id: en-semisimple-en-adj-hWvvBC9I Categories (other): English entries with incorrect language header, English terms prefixed with semi- Disambiguation of English entries with incorrect language header: 12 21 10 29 28 Disambiguation of English terms prefixed with semi-: 27 23 14 19 16 Topics: mathematics, sciences
  4. (mathematics, of a Lie algebra) Being a direct sum of simple Lie algebras. Tags: not-comparable Categories (topical): Mathematics
    Sense id: en-semisimple-en-adj-6K9sMw2Z Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 2 entries Disambiguation of English entries with incorrect language header: 12 21 10 29 28 Disambiguation of English terms prefixed with semi-: 27 23 14 19 16 Disambiguation of Pages with 2 entries: 15 28 9 31 17 Topics: mathematics, sciences
  5. (mathematics, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial. Tags: not-comparable Categories (topical): Mathematics
    Sense id: en-semisimple-en-adj-o~3BKg3I Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 2 entries Disambiguation of English entries with incorrect language header: 12 21 10 29 28 Disambiguation of English terms prefixed with semi-: 27 23 14 19 16 Disambiguation of Pages with 2 entries: 15 28 9 31 17 Topics: mathematics, sciences

Adjective [French]

Forms: semisimples [plural]
Etymology: From semi- + simple. Etymology templates: {{af|fr|semi-|simple}} semi- + simple Head templates: {{fr-adj}} semisimple (plural semisimples)
  1. (mathematics) semisimple Categories (topical): Mathematics Synonyms: semi-simple

Inflected forms

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "semi",
        "3": "simple"
      },
      "expansion": "semi- + simple",
      "name": "prefix"
    }
  ],
  "etymology_text": "From semi- + simple.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "semisimple (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "12 21 10 29 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "27 23 14 19 16",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "15 28 9 31 17",
          "kind": "other",
          "name": "Pages with 2 entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "In which each submodule is a direct summand."
      ],
      "id": "en-semisimple-en-adj-P-xK9P2i",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "module",
          "module"
        ],
        [
          "submodule",
          "submodule"
        ],
        [
          "summand",
          "summand"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of a module) In which each submodule is a direct summand."
      ],
      "raw_tags": [
        "of a module"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "12 21 10 29 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "27 23 14 19 16",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "15 28 9 31 17",
          "kind": "other",
          "name": "Pages with 2 entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "diagonalizable."
      ],
      "id": "en-semisimple-en-adj--0w7RsfT",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "diagonalizable",
          "diagonalizable"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of an algebra or ring) diagonalizable."
      ],
      "raw_tags": [
        "of an algebra or ring"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "12 21 10 29 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "27 23 14 19 16",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree."
      ],
      "id": "en-semisimple-en-adj-hWvvBC9I",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "operator",
          "operator"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "invariant",
          "invariant"
        ],
        [
          "subspace",
          "subspace"
        ],
        [
          "complement",
          "complement"
        ],
        [
          "minimal",
          "minimal"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "squarefree",
          "squarefree"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree."
      ],
      "raw_tags": [
        "of an operator or matrix"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "12 21 10 29 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "27 23 14 19 16",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "15 28 9 31 17",
          "kind": "other",
          "name": "Pages with 2 entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "Being a direct sum of simple Lie algebras."
      ],
      "id": "en-semisimple-en-adj-6K9sMw2Z",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "Lie algebra",
          "Lie algebra"
        ],
        [
          "simple",
          "simple"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of a Lie algebra) Being a direct sum of simple Lie algebras."
      ],
      "raw_tags": [
        "of a Lie algebra"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "12 21 10 29 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "27 23 14 19 16",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "15 28 9 31 17",
          "kind": "other",
          "name": "Pages with 2 entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "Being a linear algebraic group whose radical of the identity component is trivial."
      ],
      "id": "en-semisimple-en-adj-o~3BKg3I",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebraic group",
          "algebraic group"
        ],
        [
          "linear",
          "linear"
        ],
        [
          "radical",
          "radical"
        ],
        [
          "identity",
          "identity"
        ],
        [
          "trivial",
          "trivial"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial."
      ],
      "raw_tags": [
        "of an algebraic group"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "wikipedia": [
    "semisimple"
  ],
  "word": "semisimple"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "fr",
        "2": "semi-",
        "3": "simple"
      },
      "expansion": "semi- + simple",
      "name": "af"
    }
  ],
  "etymology_text": "From semi- + simple.",
  "forms": [
    {
      "form": "semisimples",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "semisimple (plural semisimples)",
      "name": "fr-adj"
    }
  ],
  "lang": "French",
  "lang_code": "fr",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "French entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "French terms prefixed with semi-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 2 entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "fr",
          "name": "Mathematics",
          "orig": "fr:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "semisimple"
      ],
      "id": "en-semisimple-fr-adj-fCG47oTO",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "semisimple",
          "semisimple#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics) semisimple"
      ],
      "synonyms": [
        {
          "word": "semi-simple"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "semisimple"
}
{
  "categories": [
    "English adjectives",
    "English entries with incorrect language header",
    "English lemmas",
    "English terms prefixed with semi-",
    "English uncomparable adjectives",
    "Pages with 2 entries"
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "semi",
        "3": "simple"
      },
      "expansion": "semi- + simple",
      "name": "prefix"
    }
  ],
  "etymology_text": "From semi- + simple.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "semisimple (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "In which each submodule is a direct summand."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "module",
          "module"
        ],
        [
          "submodule",
          "submodule"
        ],
        [
          "summand",
          "summand"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of a module) In which each submodule is a direct summand."
      ],
      "raw_tags": [
        "of a module"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "diagonalizable."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "diagonalizable",
          "diagonalizable"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of an algebra or ring) diagonalizable."
      ],
      "raw_tags": [
        "of an algebra or ring"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "operator",
          "operator"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "invariant",
          "invariant"
        ],
        [
          "subspace",
          "subspace"
        ],
        [
          "complement",
          "complement"
        ],
        [
          "minimal",
          "minimal"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "squarefree",
          "squarefree"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree."
      ],
      "raw_tags": [
        "of an operator or matrix"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "Being a direct sum of simple Lie algebras."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "Lie algebra",
          "Lie algebra"
        ],
        [
          "simple",
          "simple"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of a Lie algebra) Being a direct sum of simple Lie algebras."
      ],
      "raw_tags": [
        "of a Lie algebra"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "Being a linear algebraic group whose radical of the identity component is trivial."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebraic group",
          "algebraic group"
        ],
        [
          "linear",
          "linear"
        ],
        [
          "radical",
          "radical"
        ],
        [
          "identity",
          "identity"
        ],
        [
          "trivial",
          "trivial"
        ]
      ],
      "raw_glosses": [
        "(mathematics, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial."
      ],
      "raw_tags": [
        "of an algebraic group"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "wikipedia": [
    "semisimple"
  ],
  "word": "semisimple"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "fr",
        "2": "semi-",
        "3": "simple"
      },
      "expansion": "semi- + simple",
      "name": "af"
    }
  ],
  "etymology_text": "From semi- + simple.",
  "forms": [
    {
      "form": "semisimples",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "semisimple (plural semisimples)",
      "name": "fr-adj"
    }
  ],
  "lang": "French",
  "lang_code": "fr",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        "French adjectives",
        "French entries with incorrect language header",
        "French lemmas",
        "French terms prefixed with semi-",
        "Pages with 2 entries",
        "fr:Mathematics"
      ],
      "glosses": [
        "semisimple"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "semisimple",
          "semisimple#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics) semisimple"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "semi-simple"
    }
  ],
  "word": "semisimple"
}

Download raw JSONL data for semisimple meaning in All languages combined (3.8kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-09-22 from the enwiktionary dump dated 2024-09-20 using wiktextract (af5c55c and 66545a6). 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.