Field of fractionsとは 意味・読み方・使い方

名詞

field of fractions (複数形 fields of fractions)

1. (algebra, 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 ${\displaystyle \mathbb {Q} _{R}}$ out of ${\displaystyle R}$ is an exact parallel of the construction of the field of rational numbers ${\displaystyle \mathbb {Q} }$ out of the ring of integers ${\displaystyle \mathbb {Z} }$.

   • 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.

   • 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, Khodr Shamseddine (editor), Advances in Ultrametric Analysis: 12th International Conference on p-adic Functional Analysis, American Mathematical Society, page 23,

     We denote by ${\displaystyle {\mathcal {A}}(\mathbb {K} )}$ the ${\displaystyle \mathbb {K} }$-algebra of entire functions in ${\displaystyle \mathbb {K} }$ i.e. the set of power series with coefficients in ${\displaystyle \mathbb {K} }$ converging in all ${\displaystyle \mathbb {K} }$ and we denote by ${\displaystyle {\mathcal {M}}(\mathbb {K} )}$ the field of meromorphic functions in ${\displaystyle \mathbb {K} }$, i.e. the field of fractions of ${\displaystyle {\mathcal {A}}(\mathbb {K} )}$.