"discrete valuation ring" meaning in All languages combined

See discrete valuation ring on Wiktionary

Noun [English]

Forms: discrete valuation rings [plural]
Head templates: {{en-noun}} discrete valuation ring (plural discrete valuation rings)
  1. (algebra, ring theory) A local principal ideal domain whose unique maximal ideal is not the zero ideal. Wikipedia link: discrete valuation ring Categories (topical): Algebra Synonyms: DVR
    Sense id: en-discrete_valuation_ring-en-noun-ndlo6-hb Categories (other): English entries with incorrect language header, Pages with 1 entry Topics: algebra, mathematics, sciences

Alternative forms

{
  "forms": [
    {
      "form": "discrete valuation rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "discrete valuation ring (plural discrete valuation 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",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A local principal ideal domain whose unique maximal ideal is not the zero ideal."
      ],
      "id": "en-discrete_valuation_ring-en-noun-ndlo6-hb",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring theory",
          "ring theory"
        ],
        [
          "local",
          "local"
        ],
        [
          "principal ideal domain",
          "principal ideal domain"
        ],
        [
          "maximal ideal",
          "maximal ideal"
        ],
        [
          "zero ideal",
          "zero ideal"
        ]
      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "(algebra, ring theory) A local principal ideal domain whose unique maximal ideal is not the zero ideal."
      ],
      "synonyms": [
        {
          "word": "DVR"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "discrete valuation ring"
      ]
    }
  ],
  "word": "discrete valuation ring"
}
{
  "forms": [
    {
      "form": "discrete valuation rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "discrete valuation ring (plural discrete valuation rings)",
      "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",
        "Pages with 1 entry",
        "en:Algebra"
      ],
      "glosses": [
        "A local principal ideal domain whose unique maximal ideal is not the zero ideal."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring theory",
          "ring theory"
        ],
        [
          "local",
          "local"
        ],
        [
          "principal ideal domain",
          "principal ideal domain"
        ],
        [
          "maximal ideal",
          "maximal ideal"
        ],
        [
          "zero ideal",
          "zero ideal"
        ]
      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "(algebra, ring theory) A local principal ideal domain whose unique maximal ideal is not the zero ideal."
      ],
      "synonyms": [
        {
          "word": "DVR"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "discrete valuation ring"
      ]
    }
  ],
  "word": "discrete valuation ring"
}

Download raw JSONL data for discrete valuation ring meaning in All languages combined (1.0kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-09-01 from the enwiktionary dump dated 2024-08-20 using wiktextract (8e41825 and f99c758). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.