English

Wikibooks

Noun

integral domain ‎(plural integral domains)

1. (algebra) A commutative ring with identity not equal to zero which has no zero divisors.

   Ring R is an integral domain if and only if the polynomial ring is an integral domain.

   For any integral domain there can be derived an associated field of fractions.

Hypernyms

• commutative ring

Hyponyms

• unique factorization domain, Noetherian domain
  • principal ideal domain
    • Euclidean domain
      • field

Holonyms

• field of fractions