"selfdistributive" meaning in All languages combined

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "self",
        "3": "distributive"
      },
      "expansion": "self- + distributive",
      "name": "prefix"
    }
  ],
  "etymology_text": "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": "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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": "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",
        "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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"
}