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Field (mathematics)

Field (mathematics)1 Field (mathematics)In abstract algebra, a Field is an algebraic structure with notions of addition, subtraction, multiplication, and division,satisfying certain axioms. The most commonly used fields are the Field of real numbers, the Field of complexnumbers, and the Field of rational numbers, but there are also finite fields, fields of functions, various algebraicnumber fields, p-adic fields, and so Field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. The theory of field extensions (including Galois theory) involves the roots of polynomials with coefficients in a field; among other results, this theory leads to impossibility proofs for the classical problems of angle trisection and

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