"affine scheme" meaning in All languages combined

{
  "forms": [
    {
      "form": "affine schemes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "affine scheme (plural affine schemes)",
      "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": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of polynomial functions: a space which is the result of a particular construction beginning with an arbitrary commutative ring whereby elements of the ring can be thought of as functions on the space; a space which can be constructed in such a way. Formally: the spectrum of a commutative ring; a locally ringed space isomorphic to the spectrum of a commutative ring."
      ],
      "id": "en-affine_scheme-en-noun-jPNzsFCz",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "abstract",
          "abstract"
        ],
        [
          "geometric",
          "geometric"
        ],
        [
          "mathematics",
          "mathematics"
        ],
        [
          "generalize",
          "generalize"
        ],
        [
          "affine variety",
          "affine variety"
        ],
        [
          "qua",
          "qua"
        ],
        [
          "commutative ring",
          "commutative ring"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "function",
          "function"
        ],
        [
          "element",
          "element"
        ],
        [
          "spectrum",
          "spectrum"
        ],
        [
          "locally ringed space",
          "locally ringed space"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of polynomial functions: a space which is the result of a particular construction beginning with an arbitrary commutative ring whereby elements of the ring can be thought of as functions on the space; a space which can be constructed in such a way. Formally: the spectrum of a commutative ring; a locally ringed space isomorphic to the spectrum of a commutative ring."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "affine scheme"
}

{
  "forms": [
    {
      "form": "affine schemes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "affine scheme (plural affine schemes)",
      "name": "en-noun"
    }
  ],
  "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:Algebraic geometry"
      ],
      "glosses": [
        "An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of polynomial functions: a space which is the result of a particular construction beginning with an arbitrary commutative ring whereby elements of the ring can be thought of as functions on the space; a space which can be constructed in such a way. Formally: the spectrum of a commutative ring; a locally ringed space isomorphic to the spectrum of a commutative ring."
      ],
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "abstract",
          "abstract"
        ],
        [
          "geometric",
          "geometric"
        ],
        [
          "mathematics",
          "mathematics"
        ],
        [
          "generalize",
          "generalize"
        ],
        [
          "affine variety",
          "affine variety"
        ],
        [
          "qua",
          "qua"
        ],
        [
          "commutative ring",
          "commutative ring"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "function",
          "function"
        ],
        [
          "element",
          "element"
        ],
        [
          "spectrum",
          "spectrum"
        ],
        [
          "locally ringed space",
          "locally ringed space"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of polynomial functions: a space which is the result of a particular construction beginning with an arbitrary commutative ring whereby elements of the ring can be thought of as functions on the space; a space which can be constructed in such a way. Formally: the spectrum of a commutative ring; a locally ringed space isomorphic to the spectrum of a commutative ring."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "affine scheme"
}