"maximal ideal" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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      "coordinate_terms": [
        {
          "word": "minimal ideal"
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      "examples": [
        {
          "ref": "1994, William M. McGovern, Completely Prime Maximal Ideals and Quantization, American Mathematical Society, page 15:",
          "text": "Denote the minimal prime ideal in (b) by J#x5F;#x5C;mathsf#x7B;max#x7D;(#x5C;lambda), the unique maximal ideal of infinitesimal character #x5C;lambda.",
          "type": "quote"
        },
        {
          "text": "2004, Ayman Badawi, Abstract Algebra Manual: Problems and Solutions, Nova Science, 2nd Edition, page 87,\nLet S be the set of all prime ideals of B, and H be the set of all maximal ideals of B."
        },
        {
          "ref": "2013, Igor R. Shafarevich, Basic Algebraic Geometry 2: Schemes and Complex Manifolds, 3rd edition, Springer, page 11:",
          "text": "In particular, a prime ideal #x5C;mathfrak#x7B;p#x7D;#x5C;subsetA is a closed point of #x5C;mathrm#x7B;Spec#x7D;#x5C;A if and only if #x5C;mathfrak#x7B;p#x7D; is a maximal ideal.",
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        }
      ],
      "glosses": [
        "An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure)."
      ],
      "id": "en-maximal_ideal-en-noun-7Yvnvy22",
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      "qualifier": "ring theory",
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        "(algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure)."
      ],
      "related": [
        {
          "word": "maximal left ideal"
        },
        {
          "word": "maximal right ideal"
        }
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        "maximal ideal"
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  "word": "maximal ideal"
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          "ref": "1994, William M. McGovern, Completely Prime Maximal Ideals and Quantization, American Mathematical Society, page 15:",
          "text": "Denote the minimal prime ideal in (b) by J#x5F;#x5C;mathsf#x7B;max#x7D;(#x5C;lambda), the unique maximal ideal of infinitesimal character #x5C;lambda.",
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          "text": "2004, Ayman Badawi, Abstract Algebra Manual: Problems and Solutions, Nova Science, 2nd Edition, page 87,\nLet S be the set of all prime ideals of B, and H be the set of all maximal ideals of B."
        },
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          "ref": "2013, Igor R. Shafarevich, Basic Algebraic Geometry 2: Schemes and Complex Manifolds, 3rd edition, Springer, page 11:",
          "text": "In particular, a prime ideal #x5C;mathfrak#x7B;p#x7D;#x5C;subsetA is a closed point of #x5C;mathrm#x7B;Spec#x7D;#x5C;A if and only if #x5C;mathfrak#x7B;p#x7D; is a maximal ideal.",
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        "An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure)."
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        "(algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure)."
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