"Noetherian ring" meaning in English

{
  "etymology_text": "Named after German mathematician Emmy Noether (1882–1935).",
  "forms": [
    {
      "form": "Noetherian rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Noetherian ring (plural Noetherian rings)",
      "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",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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            "Sciences",
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      ],
      "derived": [
        {
          "word": "left Noetherian ring"
        },
        {
          "word": "right Noetherian ring"
        }
      ],
      "examples": [
        {
          "ref": "1986, Hideyuki Matsumura, translated by M. Reid, Commutative Ring Theory, Paperback edition, Cambridge University Press, published 1989, page ix",
          "text": "The central position occupied by Noetherian rings in commutative ring theory became evident from her work.",
          "type": "quotation"
        },
        {
          "ref": "2000, John C. McConnell, James Christopher Robson, Lance W. Small, Noncommutative Noetherian Rings, 2nd edition, American Mathematical Society, page 97",
          "text": "In this chapter the focus moves from semiprime rings to general Noetherian rings, although it does concentrate on prime and semiprime ideals.",
          "type": "quotation"
        },
        {
          "text": "2004, K. R. Goodearl, Introduction to the Second Edition, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 2nd Edition, page viii,\nDuring this same period, the explosive growth of the area of quantum groups provided a large new crop of noetherian rings to be analyzed, and thus gave major impetus to research in noetherian ring theory."
        }
      ],
      "glosses": [
        "A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated)."
      ],
      "hyponyms": [
        {
          "sense": "Noetherian domain",
          "word": "Dedekind domain"
        },
        {
          "word": "Artinian ring"
        }
      ],
      "id": "en-Noetherian_ring-en-noun-QnU228kn",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "commutative ring",
          "commutative ring"
        ],
        [
          "ideal",
          "ideal"
        ],
        [
          "finitely generated",
          "finitely generated"
        ],
        [
          "noncommutative",
          "noncommutative"
        ],
        [
          "left-Noetherian",
          "left-Noetherian"
        ],
        [
          "left ideal",
          "left ideal"
        ],
        [
          "right-Noetherian",
          "right-Noetherian"
        ],
        [
          "right ideal",
          "right ideal"
        ]
      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "(algebra, ring theory) A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated)."
      ],
      "related": [
        {
          "word": "left-Noetherian"
        },
        {
          "word": "Noetherian"
        },
        {
          "word": "right-Noetherian"
        }
      ],
      "synonyms": [
        {
          "word": "noetherian ring"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Emmy Noether",
        "Noetherian ring"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/"
    }
  ],
  "word": "Noetherian ring"
}

{
  "derived": [
    {
      "word": "left Noetherian ring"
    },
    {
      "word": "right Noetherian ring"
    }
  ],
  "etymology_text": "Named after German mathematician Emmy Noether (1882–1935).",
  "forms": [
    {
      "form": "Noetherian rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Noetherian ring (plural Noetherian rings)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "sense": "Noetherian domain",
      "word": "Dedekind domain"
    },
    {
      "word": "Artinian ring"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "left-Noetherian"
    },
    {
      "word": "Noetherian"
    },
    {
      "word": "right-Noetherian"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
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        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with IPA pronunciation",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "IPA for English using .ˈ or .ˌ",
        "en:Algebra"
      ],
      "examples": [
        {
          "ref": "1986, Hideyuki Matsumura, translated by M. Reid, Commutative Ring Theory, Paperback edition, Cambridge University Press, published 1989, page ix",
          "text": "The central position occupied by Noetherian rings in commutative ring theory became evident from her work.",
          "type": "quotation"
        },
        {
          "ref": "2000, John C. McConnell, James Christopher Robson, Lance W. Small, Noncommutative Noetherian Rings, 2nd edition, American Mathematical Society, page 97",
          "text": "In this chapter the focus moves from semiprime rings to general Noetherian rings, although it does concentrate on prime and semiprime ideals.",
          "type": "quotation"
        },
        {
          "text": "2004, K. R. Goodearl, Introduction to the Second Edition, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 2nd Edition, page viii,\nDuring this same period, the explosive growth of the area of quantum groups provided a large new crop of noetherian rings to be analyzed, and thus gave major impetus to research in noetherian ring theory."
        }
      ],
      "glosses": [
        "A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated)."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "commutative ring",
          "commutative ring"
        ],
        [
          "ideal",
          "ideal"
        ],
        [
          "finitely generated",
          "finitely generated"
        ],
        [
          "noncommutative",
          "noncommutative"
        ],
        [
          "left-Noetherian",
          "left-Noetherian"
        ],
        [
          "left ideal",
          "left ideal"
        ],
        [
          "right-Noetherian",
          "right-Noetherian"
        ],
        [
          "right ideal",
          "right ideal"
        ]
      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "(algebra, ring theory) A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated)."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Emmy Noether",
        "Noetherian ring"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/"
    }
  ],
  "synonyms": [
    {
      "word": "noetherian ring"
    }
  ],
  "word": "Noetherian ring"
}