field of fractions

plural fields of fractions

1. ring theoryalgebraThe 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.

   2 more examples

   1989, Nicolas Bourbaki, 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.

   We denote by #92;mathcal#123;A#125;(#92;mathbb#123;K#125;) the #92;mathbb#123;K#125;-algebra of entire functions in #92;mathbb#123;K#125; i.e. the set of power series with coefficients in #92;mathbb#123;K#125; converging in all #92;mathbb#123;K#125; and we denote by #92;mathcal#123;M#125;(#92;mathbb#123;K#125;) the field of meromorphic functions in #92;mathbb#123;K#125;, i.e. the field of fractions of #92;mathcal#123;A#125;(#92;mathbb#123;K#125;).

   2013, Jean-Paul Bézivin, Kamal Boussaf, Alain Escassut, “Some old and new results on the zeros of the derivative of a p-adic meromorphic function”, in Khodr Shamseddine, editor, Advances in Ultrametric Analysis: 12th International Conference on p-adic Functional Analysis, American Mathematical Society, page 23

   Synonyms: field of quotients, fraction field, quotient field