"ring of fractions" meaning in All languages combined

{
  "forms": [
    {
      "form": "rings of fractions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "rings of fractions"
      },
      "expansion": "ring of fractions (plural rings of fractions)",
      "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 ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0."
      ],
      "hyponyms": [
        {
          "word": "field of fractions"
        },
        {
          "word": "total ring of fractions"
        },
        {
          "word": "localization"
        }
      ],
      "id": "en-ring_of_fractions-en-noun-4G53KYKP",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "fraction",
          "fraction"
        ],
        [
          "commutative",
          "commutative ring"
        ],
        [
          "unital",
          "unital"
        ],
        [
          "field of fractions",
          "field of fractions"
        ]
      ],
      "raw_glosses": [
        "(algebra) A ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ring of fractions"
}

{
  "forms": [
    {
      "form": "rings of fractions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "rings of fractions"
      },
      "expansion": "ring of fractions (plural rings of fractions)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "field of fractions"
    },
    {
      "word": "total ring of fractions"
    },
    {
      "word": "localization"
    }
  ],
  "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 ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "fraction",
          "fraction"
        ],
        [
          "commutative",
          "commutative ring"
        ],
        [
          "unital",
          "unital"
        ],
        [
          "field of fractions",
          "field of fractions"
        ]
      ],
      "raw_glosses": [
        "(algebra) A ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ring of fractions"
}