Commutative algebra | Field (mathematics)

Field of fractions

In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The construction of the field of fractions is modeled on the relationship between the integral domain of integers and the field of rational numbers. Intuitively, it consists of ratios between integral domain elements. The field of fractions of is sometimes denoted by or , and the construction is sometimes also called the fraction field, field of quotients, or quotient field of . All four are in common usage, but are not to be confused with the quotient of a ring by an ideal, which is a quite different concept. For a commutative ring which is not an integral domain, the analogous construction is called the localization or ring of quotients. (Wikipedia).

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Field Theory: Polynomials

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From playlist Basics: Field Theory

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What is a fraction?

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From playlist Fraction Concepts

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Algebraic Fractions (1 of 2: Addition & Subtraction)

More resources available at www.misterwootube.com

From playlist Further Algebraic Techniques

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From playlist Abstract Algebra

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From playlist Real Numbers

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From playlist Basics: Field Theory

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From playlist Math Foundations

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From playlist Log Volume Computations

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From playlist MFEM Community Workshop 2022

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From playlist Advances in Graphene, Majorana fermions, Quantum computation

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Abstract Algebra | The field of fractions of an integral domain.

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From playlist Abstract Algebra

Related pages

Prime ideal | Quotient ring | Integral domain | Zero ring | Zero divisor | Fraction | Semifield | Category of fields | Reflective subcategory | Isomorphism | Rational number | Rng (algebra) | Ore condition | Polynomial ring | Equivalence class | Gaussian integer | Field (mathematics) | Integer | Ring homomorphism | Localization (commutative algebra) | Embedding | Ring (mathematics) | Category theory | Projective line over a ring | Category (mathematics) | Functor | Equivalence relation | Abstract algebra | Semiring | Total ring of fractions | Universal property | Gaussian rational | Commutative ring