algebraic field

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• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …   Wikipedia

• Algebraic combinatorics — is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. It is one of the… …   Wikipedia

• Algebraic statistics — is a fairly recent field of statistics which utilizes the tools of algebraic geometry and commutative algebra in order to study problems related to discrete random variables with finite state spaces. Such problems include parameter estimation,… …   Wikipedia

• Algebraic holography — Algebraic holography, also sometimes called Rehren duality , is an attempt to understand the holographic principle of quantum gravity within the framework of algebraic quantum field theory, due to Karl Henning Rehren. It is sometimes described as …   Wikipedia

• Algebraic biology — applies the algebraic methods of symbolic computation to the study of biological problems, especially in genomics, proteomics, analysis of molecular structures and study of genes.UsageComputations in the field of biology are done in order to… …   Wikipedia

• Field — or fields may refer to: * Field (agriculture), an area of land used to cultivate crops for agricultural purposes * Field of study, a branch of knowledge * Playing field, in sports, the area in which the sport is played * Visual field or field of… …   Wikipedia

• Algebraic Geometry (book) — Algebraic Geometry is an influential algebraic geometry textbook written by Robin Hartshorne and published by Springer Verlag in 1977. It was the first extended treatment of scheme theory written as a text intended to be accessible to graduate… …   Wikipedia

• field — [fēld] n. [ME feld < OE, akin to Ger feld, Du veld < IE * pelt < base * pele , * pla , flat and broad > L planus, plane, Gr palamē, flat hand] 1. a wide stretch of open land; plain 2. a piece of cleared land, set off or enclosed, for… …   English World dictionary

• Field theory — may refer to: *Field theory (mathematics), the theory of the algebraic concept of field *Field theory (physics), a physical theory which employs fields in the physical sense *Field theory (psychology), a psychological theory which examines… …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia