trivial field
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Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… … 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
Trivial representation — In the mathematical field of representation theory, a trivial representation is a representation ( V , phi; ) of a group G on which all elements of G act as the identity mapping of V . A trivial representation of an associative or Lie algebra is… … Wikipedia
Field-effect transistor — FET redirects here. For other uses, see FET (disambiguation). High power N channel field effect transistor The field effect transistor (FET) is a transistor that relies on an electric field to control the shape and hence the conductivity of a… … Wikipedia
Field arithmetic — In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… … Wikipedia
Quasi-algebraically closed field — In mathematics, a field F is called quasi algebraically closed (or C1) if for every non constant homogeneous polynomial P over F has a non trivial zero provided the number of its variables is more than its degree. In other words, if P is a non… … Wikipedia
Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… … Wikipedia
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
Scalar field theory — In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a scalar , in contrast to a vector or tensor field. The quanta of the… … Wikipedia
Ramond-Ramond field — In theoretical physics, Ramond Ramond fields are differential form fields in the 10 dimensional spacetime of type II supergravity theories, which are the classical limits of type II string theory. The ranks of the fields depend on which type II… … Wikipedia
Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… … Wikipedia
