See selfdistributive in All languages combined, or Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "self", "3": "distributive" }, "expansion": "self- + distributive", "name": "prefix" } ], "etymology_text": "From self- + distributive.", "head_templates": [ { "args": { "1": "-" }, "expansion": "selfdistributive (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "English terms prefixed with self-", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "2015, Camille Laurent-Gengoux, Friedrich Wagemann, “Lie rackoids”, in arXiv:", "text": "Its main ingredient is a selfdistributive product on the manifold of bisections of a smooth precategory. We show that the tangent algebroid of a Lie rackoid is a Leibniz algebroid and that Lie groupoids gives rise via conjugation to a Lie rackoid.", "type": "quote" }, { "ref": "2019, Petr Vojtěchovský, Murray R. Bremner, J. Scott Carter, Nonassociative Mathematics and its Applications, page 70:", "text": "The aim of this text is to survey some aspects of selfdistributive algebra, with a special emphasis on the involved word problems.", "type": "quote" } ], "glosses": [ "Having the property (of an operation) of being distributive with respect to itself. Thus, an operator ◦ is left selfdistributive iff x◦(y◦z) = (x◦y)◦(x◦z), and is right selfdistributive iff (x◦y)◦z = (x◦z)◦(y◦z), for all x, y, z." ], "id": "en-selfdistributive-en-adj-CU4skBuo", "links": [ [ "mathematics", "mathematics" ], [ "distributive", "distributive" ] ], "raw_glosses": [ "(mathematics) Having the property (of an operation) of being distributive with respect to itself. Thus, an operator ◦ is left selfdistributive iff x◦(y◦z) = (x◦y)◦(x◦z), and is right selfdistributive iff (x◦y)◦z = (x◦z)◦(y◦z), for all x, y, z." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] } ], "word": "selfdistributive" }
{ "etymology_templates": [ { "args": { "1": "en", "2": "self", "3": "distributive" }, "expansion": "self- + distributive", "name": "prefix" } ], "etymology_text": "From self- + distributive.", "head_templates": [ { "args": { "1": "-" }, "expansion": "selfdistributive (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English terms prefixed with self-", "English terms with quotations", "English uncomparable adjectives", "Pages with 1 entry", "Pages with entries", "en:Mathematics" ], "examples": [ { "ref": "2015, Camille Laurent-Gengoux, Friedrich Wagemann, “Lie rackoids”, in arXiv:", "text": "Its main ingredient is a selfdistributive product on the manifold of bisections of a smooth precategory. We show that the tangent algebroid of a Lie rackoid is a Leibniz algebroid and that Lie groupoids gives rise via conjugation to a Lie rackoid.", "type": "quote" }, { "ref": "2019, Petr Vojtěchovský, Murray R. Bremner, J. Scott Carter, Nonassociative Mathematics and its Applications, page 70:", "text": "The aim of this text is to survey some aspects of selfdistributive algebra, with a special emphasis on the involved word problems.", "type": "quote" } ], "glosses": [ "Having the property (of an operation) of being distributive with respect to itself. Thus, an operator ◦ is left selfdistributive iff x◦(y◦z) = (x◦y)◦(x◦z), and is right selfdistributive iff (x◦y)◦z = (x◦z)◦(y◦z), for all x, y, z." ], "links": [ [ "mathematics", "mathematics" ], [ "distributive", "distributive" ] ], "raw_glosses": [ "(mathematics) Having the property (of an operation) of being distributive with respect to itself. Thus, an operator ◦ is left selfdistributive iff x◦(y◦z) = (x◦y)◦(x◦z), and is right selfdistributive iff (x◦y)◦z = (x◦z)◦(y◦z), for all x, y, z." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] } ], "word": "selfdistributive" }
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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.
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