"principal ideal ring" meaning in English

See principal ideal ring in All languages combined, or Wiktionary

Noun

Forms: principal ideal rings [plural]
Head templates: {{en-noun}} principal ideal ring (plural principal ideal rings)
  1. (algebra, ring theory) A commutative ring in which every ideal is a principal ideal. Categories (topical): Algebra, Ring theory
    Sense id: en-principal_ideal_ring-en-noun-aNhk27MT Disambiguation of Ring theory: 53 47 Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms with non-redundant non-automated sortkeys Disambiguation of English entries with incorrect language header: 54 46 Disambiguation of English entries with topic categories using raw markup: 70 30 Disambiguation of English terms with non-redundant non-automated sortkeys: 58 42 Topics: algebra, mathematics, sciences
  2. (algebra, ring theory) A noncommutative ring in which every left ideal is a principal ideal and so is every right ideal. Categories (topical): Algebra, Ring theory
    Sense id: en-principal_ideal_ring-en-noun-bA7K~Ui0 Disambiguation of Ring theory: 53 47 Categories (other): English entries with incorrect language header Disambiguation of English entries with incorrect language header: 54 46 Topics: algebra, mathematics, sciences
The following are not (yet) sense-disambiguated
Hyponyms: principal ideal domain

Inflected forms

Download JSON data for principal ideal ring meaning in English (3.0kB)

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). 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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