See semisimple in All languages combined, or Wiktionary
Download JSON data for semisimple meaning in English (5.3kB)
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"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" } ], "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" } ], "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" } ], "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" }
{ "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English terms prefixed with semi-", "English uncomparable adjectives" ], "etymology_templates": [ { "args": { "1": "en", "2": "semi", "3": "simple" }, "expansion": "semi- + simple", "name": "prefix" } ], "etymology_text": "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" }
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