"Jordan algebra" meaning in English

{
  "etymology_text": "Introduced by Pascual Jordan.",
  "forms": [
    {
      "form": "Jordan algebras",
      "tags": [
        "plural"
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      "glosses": [
        "A non-associative algebra over a field whose product satisfies the axioms (i) xy=yx (the commutative law) and (ii) (xy)(xx)=x(y(xx)) (the Jordan identity)."
      ],
      "hyponyms": [
        {
          "word": "Albert algebra"
        }
      ],
      "id": "en-Jordan_algebra-en-noun-9DyRMVti",
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          "mathematics",
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          "associative",
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        [
          "algebra",
          "algebra"
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        [
          "field",
          "field"
        ],
        [
          "product",
          "product"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "commutative",
          "commutative"
        ],
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          "Jordan identity",
          "Jordan identity"
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      ],
      "raw_glosses": [
        "(mathematics) A non-associative algebra over a field whose product satisfies the axioms (i) xy=yx (the commutative law) and (ii) (xy)(xx)=x(y(xx)) (the Jordan identity)."
      ],
      "topics": [
        "mathematics",
        "sciences"
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      "wikipedia": [
        "Jordan algebra"
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  ],
  "word": "Jordan algebra"
}

{
  "etymology_text": "Introduced by Pascual Jordan.",
  "forms": [
    {
      "form": "Jordan algebras",
      "tags": [
        "plural"
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    }
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    }
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  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A non-associative algebra over a field whose product satisfies the axioms (i) xy=yx (the commutative law) and (ii) (xy)(xx)=x(y(xx)) (the Jordan identity)."
      ],
      "links": [
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          "algebra",
          "algebra"
        ],
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          "field",
          "field"
        ],
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          "product",
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          "axiom",
          "axiom"
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          "commutative",
          "commutative"
        ],
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          "Jordan identity",
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      "raw_glosses": [
        "(mathematics) A non-associative algebra over a field whose product satisfies the axioms (i) xy=yx (the commutative law) and (ii) (xy)(xx)=x(y(xx)) (the Jordan identity)."
      ],
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        "mathematics",
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