"local ring" meaning in English

See local ring in All languages combined, or Wiktionary

Noun

Forms: local rings [plural]
Head templates: {{en-noun}} local ring (plural local rings)
  1. (algebra) A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal. Categories (topical): Algebra, Mathematics, Ring theory Hyponyms: simple ring, field
    Sense id: en-local_ring-en-noun-t04Kt7RG Disambiguation of Mathematics: 57 43 Disambiguation of Ring theory: 64 36 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 57 43 Disambiguation of Pages with 1 entry: 60 40 Disambiguation of Pages with entries: 60 40 Topics: algebra, mathematics, sciences
  2. (networking) The non-routing segment of a token ring network. Categories (topical): Networking
    Sense id: en-local_ring-en-noun-BB8KU0si Topics: computing, engineering, mathematics, natural-sciences, networking, physical-sciences, sciences

Inflected forms

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  "lang_code": "en",
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  "senses": [
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      "examples": [
        {
          "text": "The unique maximal ideal of a (commutative) local ring contains all of the zero divisors of such ring, and all elements of the ring outside of it are units. Then in a local ring, the sum of any two zero divisors is also a zero divisor. Contrapositively, if two ring elements add up to a unit then one of them must be a unit as well. A simple example of a local ring is #92;mathbb#123;Z#125;#95;8.",
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        "A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal."
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        "(algebra) A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal."
      ],
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        "algebra",
        "mathematics",
        "sciences"
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        "The non-routing segment of a token ring network."
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          "text": "The unique maximal ideal of a (commutative) local ring contains all of the zero divisors of such ring, and all elements of the ring outside of it are units. Then in a local ring, the sum of any two zero divisors is also a zero divisor. Contrapositively, if two ring elements add up to a unit then one of them must be a unit as well. A simple example of a local ring is #92;mathbb#123;Z#125;#95;8.",
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        "(algebra) A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal."
      ],
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        "algebra",
        "mathematics",
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      ],
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        "(networking) The non-routing segment of a token ring network."
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}

Download raw JSONL data for local ring meaning in English (1.9kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-25 from the enwiktionary dump dated 2025-01-20 using wiktextract (c15a5ce and 5c11237). 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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