"maximal ideal" meaning in All languages combined

{
  "forms": [
    {
      "form": "maximal ideals",
      "tags": [
        "plural"
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  "head_templates": [
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      "expansion": "maximal ideal (plural maximal ideals)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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        }
      ],
      "coordinate_terms": [
        {
          "word": "minimal ideal"
        }
      ],
      "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": "quotation"
        },
        {
          "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.",
          "type": "quotation"
        }
      ],
      "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",
      "links": [
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          "algebra",
          "algebra"
        ],
        [
          "ideal",
          "ideal#English"
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      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "(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"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "maximal ideal"
      ]
    }
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  "word": "maximal ideal"
}

{
  "coordinate_terms": [
    {
      "word": "minimal ideal"
    }
  ],
  "forms": [
    {
      "form": "maximal ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "maximal ideal (plural maximal ideals)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "maximal left ideal"
    },
    {
      "word": "maximal right ideal"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
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        "English nouns",
        "English terms with quotations",
        "en:Algebra"
      ],
      "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": "quotation"
        },
        {
          "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.",
          "type": "quotation"
        }
      ],
      "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)."
      ],
      "links": [
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          "algebra"
        ],
        [
          "ideal",
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        ]
      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "(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)."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
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      "wikipedia": [
        "maximal ideal"
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    }
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  "word": "maximal ideal"
}