"affine scheme" meaning in All languages combined

{
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    {
      "form": "affine schemes",
      "tags": [
        "plural"
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    }
  ],
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      "expansion": "affine scheme (plural affine schemes)",
      "name": "en-noun"
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "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."
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        [
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        [
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        [
          "affine variety",
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        ],
        [
          "qua",
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        [
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        ],
        [
          "polynomial",
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        ],
        [
          "function",
          "function"
        ],
        [
          "element",
          "element"
        ],
        [
          "spectrum",
          "spectrum"
        ],
        [
          "locally ringed space",
          "locally ringed space"
        ]
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      "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."
      ],
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        "algebraic-geometry",
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        "sciences"
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  ],
  "word": "affine scheme"
}

{
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      "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."
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      "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."
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}