"free module" meaning in English

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      "form": "free modules",
      "tags": [
        "plural"
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    }
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      "expansion": "free module (plural free modules)",
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  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)"
      ],
      "hypernyms": [
        {
          "word": "projective module"
        }
      ],
      "hyponyms": [
        {
          "word": "free abelian group"
        },
        {
          "word": "vector space"
        }
      ],
      "id": "en-free_module-en-noun-Pq8m8hrK",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "module",
          "module#English"
        ],
        [
          "basis",
          "basis#English"
        ],
        [
          "tuples",
          "tuple#English"
        ],
        [
          "ring",
          "ring#English"
        ],
        [
          "identities",
          "identities"
        ],
        [
          "rank",
          "rank#English"
        ],
        [
          "direct sum",
          "direct sum"
        ]
      ],
      "raw_glosses": [
        "(algebra) A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)"
      ],
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        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "free module"
      ]
    }
  ],
  "word": "free module"
}

{
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    {
      "form": "free modules",
      "tags": [
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      "expansion": "free module (plural free modules)",
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  "hypernyms": [
    {
      "word": "projective module"
    }
  ],
  "hyponyms": [
    {
      "word": "free abelian group"
    },
    {
      "word": "vector space"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)"
      ],
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        [
          "algebra",
          "algebra"
        ],
        [
          "module",
          "module#English"
        ],
        [
          "basis",
          "basis#English"
        ],
        [
          "tuples",
          "tuple#English"
        ],
        [
          "ring",
          "ring#English"
        ],
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          "identities",
          "identities"
        ],
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          "rank",
          "rank#English"
        ],
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          "direct sum",
          "direct sum"
        ]
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      "raw_glosses": [
        "(algebra) A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)"
      ],
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        "mathematics",
        "sciences"
      ],
      "wikipedia": [
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  "word": "free module"
}