Field of fractions

English

Noun

1. Template:Lb The smallest Template:L in which a given Template:L can be embedded.
   • 1971 [Wadsworth Publishing], Allan Clark, Elements of Abstract Algebra, 1984, Dover, page 175,

     The general construction of the field of fractions ${\mathbb{Q}}_R$ out of $R$ is an exact parallel of the construction of the field of rational numbers $\mathbb{Q}$ out of the ring of integers $\mathbb{Z}$.

   • 1989, Template:W, Commutative Algebra: Chapters 1-7, [1985, Éléments de Mathématique Algèbre Commutative, 1-4 et 5-7, Masson], Springer, page 535,

     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.

   • Template:Quote-book

Usage notes

Loosely speaking, the minimal embedding field must include the inverse of each nonzero element of the original ring and all multiples of each inverse.

May be denoted Frac(R) or Quot(R).

The synonym Template:M risks confusion with Template:M or quotient of a ring by an ideal, a quite different concept.

Synonyms

• Template:L, Template:L, Template:L

Hypernyms

• Template:L