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Field (mathematics)
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Geliefert zwischen Fr., 23.01.2026 und Mo., 26.01.2026
Details
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 complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, various algebraic number fields, p-adic fields, and so forth. 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 squaring the circle with a compass and straightedge, as well as a proof of the Abel Ruffini theorem on the insolubility of quintic equations. In modern mathematics, the theory of fields (or field theory) plays an essential role in number theory and algebraic geometry. As an algebraic structure, every field is a ring, but not every ring is a field.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130615727
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T18mm
- Jahr 2010
- EAN 9786130615727
- Format Fachbuch
- ISBN 978-613-0-61572-7
- Titel Field (mathematics)
- Untertitel Abstract algebra, Algebraic structure, Addition, Subtraction, Multiplication, Division (mathematics), Real number, Complex number, Rational number, Finite field, Function (mathematics)
- Gewicht 457g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 296
- Genre Mathematik
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