"noncommutative" meaning in English

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "non",
        "3": "commutative"
      },
      "expansion": "non- + commutative",
      "name": "prefix"
    }
  ],
  "etymology_text": "From non- + commutative.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "noncommutative (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 non-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Icelandic translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Ukrainian translations",
          "parents": [],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "noncommutative geometry"
        }
      ],
      "glosses": [
        "Not having commutativity of all elements under its operation."
      ],
      "id": "en-noncommutative-en-adj-5wrVhqR-",
      "links": [
        [
          "algebraic",
          "algebraic"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "commutativity",
          "commutativity"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(of an algebraic structure) Not having commutativity of all elements under its operation."
      ],
      "raw_tags": [
        "of an algebraic structure"
      ],
      "tags": [
        "not-comparable"
      ],
      "translations": [
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "not commutative",
          "tags": [
            "masculine"
          ],
          "word": "óvíxlinn"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "nekommutativnyj",
          "sense": "not commutative",
          "word": "некоммутативный"
        },
        {
          "code": "uk",
          "lang": "Ukrainian",
          "roman": "nekomutatyvnyj",
          "sense": "not commutative",
          "word": "некомутативний"
        }
      ]
    }
  ],
  "word": "noncommutative"
}

{
  "derived": [
    {
      "word": "noncommutative geometry"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "non",
        "3": "commutative"
      },
      "expansion": "non- + commutative",
      "name": "prefix"
    }
  ],
  "etymology_text": "From non- + commutative.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "noncommutative (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 non-",
        "English uncomparable adjectives",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Icelandic translations",
        "Terms with Russian translations",
        "Terms with Ukrainian translations"
      ],
      "glosses": [
        "Not having commutativity of all elements under its operation."
      ],
      "links": [
        [
          "algebraic",
          "algebraic"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "commutativity",
          "commutativity"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(of an algebraic structure) Not having commutativity of all elements under its operation."
      ],
      "raw_tags": [
        "of an algebraic structure"
      ],
      "tags": [
        "not-comparable"
      ]
    }
  ],
  "translations": [
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "not commutative",
      "tags": [
        "masculine"
      ],
      "word": "óvíxlinn"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "nekommutativnyj",
      "sense": "not commutative",
      "word": "некоммутативный"
    },
    {
      "code": "uk",
      "lang": "Ukrainian",
      "roman": "nekomutatyvnyj",
      "sense": "not commutative",
      "word": "некомутативний"
    }
  ],
  "word": "noncommutative"
}