field of fractions

Noun

 * 1)  The smallest  in which a given  can be embedded.
 * 2) * 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 $$\mathbb{Z}$$.
 * 1) * 1989,, 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.

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 risks confusion with  or quotient of a ring by an ideal, a quite different concept.