"free module" meaning in English

{
  "forms": [
    {
      "form": "free modules",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "free module (plural free modules)",
      "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": [
        "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.)"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "free module"
      ]
    }
  ],
  "word": "free module"
}

{
  "forms": [
    {
      "form": "free modules",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "free module (plural free modules)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "projective module"
    }
  ],
  "hyponyms": [
    {
      "word": "free abelian group"
    },
    {
      "word": "vector space"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Algebra"
      ],
      "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.)"
      ],
      "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.)"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "free module"
      ]
    }
  ],
  "word": "free module"
}