"additive identity" meaning in English

{
  "forms": [
    {
      "form": "additive identities",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "additive identity (plural additive identities)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure."
      ],
      "id": "en-additive_identity-en-noun-wYZcRRg0",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "identity",
          "identity"
        ],
        [
          "additive operation",
          "additive operation"
        ]
      ],
      "raw_glosses": [
        "(algebra) An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure."
      ],
      "related": [
        {
          "word": "multiplicative identity"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "da",
          "lang": "Danish",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "nulelement"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "mathematics",
          "word": "yhteenlaskun neutraalialkio"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "additive Identität"
        },
        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "mathematics",
          "word": "additív egységelem"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "identidade aditiva"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "neutro aditivo"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "mathematics",
          "word": "additativ identitet"
        },
        {
          "code": "th",
          "lang": "Thai",
          "sense": "mathematics",
          "word": "เอกลักษณ์การบวก"
        }
      ],
      "wikipedia": [
        "additive identity"
      ]
    }
  ],
  "word": "additive identity"
}

{
  "forms": [
    {
      "form": "additive identities",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "additive identity (plural additive identities)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "multiplicative identity"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Algebra"
      ],
      "glosses": [
        "An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "identity",
          "identity"
        ],
        [
          "additive operation",
          "additive operation"
        ]
      ],
      "raw_glosses": [
        "(algebra) An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "additive identity"
      ]
    }
  ],
  "translations": [
    {
      "code": "da",
      "lang": "Danish",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "nulelement"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "mathematics",
      "word": "yhteenlaskun neutraalialkio"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "additive Identität"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "mathematics",
      "word": "additív egységelem"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "identidade aditiva"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "neutro aditivo"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "mathematics",
      "word": "additativ identitet"
    },
    {
      "code": "th",
      "lang": "Thai",
      "sense": "mathematics",
      "word": "เอกลักษณ์การบวก"
    }
  ],
  "word": "additive identity"
}