unique factorization ring in English

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{
  "forms": [
    {
      "form": "unique factorization rings",
      "tags": [
        "plural"
      ]
    }
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  "head_templates": [
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      "args": {},
      "expansion": "unique factorization ring (plural unique factorization rings)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes."
      ],
      "hyponyms": [
        {
          "word": "unique factorization domain"
        }
      ],
      "id": "en-unique_factorization_ring-en-noun-lcXzSR6O",
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          "ring",
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      "qualifier": "ring theory",
      "raw_glosses": [
        "(algebra, ring theory) A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "unique factorization ring"
}

[Show JSON for raw wiktextract data ▼] [Hide JSON for raw wiktextract data ▲]

{
  "forms": [
    {
      "form": "unique factorization rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "unique factorization ring (plural unique factorization rings)",
      "name": "en-noun"
    }
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  "hyponyms": [
    {
      "word": "unique factorization domain"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes."
      ],
      "links": [
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          "algebra"
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          "ring"
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        "(algebra, ring theory) A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
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    }
  ],
  "word": "unique factorization ring"
}

Download raw JSONL data for unique factorization ring meaning in English (1.3kB)

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.

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"unique factorization ring" meaning in English

Noun

Inflected forms