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Definition 2026

principal_ideal_domain

principal ideal domain

English

Noun

principal ideal domain ‎(plural principal ideal domains)

(algebra) An integral domain in which every ideal is a principal ideal.

Abbreviations

PID

Hypernyms

unique factorization domain, Noetherian domain
- integral domain
  - commutative ring
Dedekind domain
principal ideal ring
Bézout domain

Hyponyms

Euclidean domain
- field