field of fractions

Noun

field of fractions (plural fields of fractions)

1. (ring theory) The smallest field in which a given ring can be embedded.
   • 1971 [Wadsworth Publishing], Allan Clark, Elements of Abstract Algebra, 1984, Dover, page 175,
     The general construction of the field of fractions ℚ_R out of R is an exact parallel of the construction of the field of rational numbers ℚ out of the ring of integers ℤ.
   • In this no., A and B denote two integrally closed Noetherian domains such that A ⊂ B and B is a finitely generated A-module and K and L the fields of fractions of A and B respectively.1989, Nicolas Bourbaki, Commutative Algebra: Chapters 1-7, [1985, Éléments de Mathématique Algèbre Commutative, 1-4 et 5-7, Masson], Springer, page 535

   Synonyms:

   field of quotients, fraction field, quotient field