field of fractions
Noun
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Noun
field of fractions
- (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 \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, 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 \mathcal{A}(\mathbb{K}) the \mathbb{K}-algebra of entire functions in \mathbb{K} i.e. the set of power series with coefficients in \mathbb{K} converging in all \mathbb{K} and we denote by \mathcal{M}(\mathbb{K}) the field of meromorphic functions in \mathbb{K}, i.e. the field of fractions of \mathcal{A}(\mathbb{K}).
- 1971 [Wadsworth Publishing], Allan Clark, Elements of Abstract Algebra, 1984, Dover, page 175 ↗,
- field of quotients, fraction field, quotient field
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