In mathematics, a field K is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation v and...

Local field potentials (LFP) are transient electrical signals generated in nerves and other tissues by the summed and synchronous electrical activity...

mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which...

(-dimensional) local field is an important example of a complete discrete valuation field. Such fields are also sometimes called multi-dimensional local fields. On...

into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification...

an area of the body Local class field theory, the study of abelian extensions of local fields Local field, a special type of field that is a locally compact...

of local fields where a more detailed analysis can be carried out with the aid of tools such as ramification groups. In this article, a local field is...

known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational...

mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...

Field electron emission, also known as field emission (FE) and electron field emission, is emission of electrons induced by an electrostatic field. The...

groups over local fields (with different subcases corresponding to archimedean local fields, p-adic local fields, and completions of function fields) Automorphic...

class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global...

the central nervous system at all levels, and include spike trains, local field potentials and large-scale oscillations which can be measured by electroencephalography...

moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. Note that the local electric field seen by a molecule...

metricPages displaying wikidata descriptions as a fallback Local field – Locally compact topological field Locally compact group – topological group G for which...

extensions of a valuation of a field K to an extension field of K. This generalizes the notions in algebraic number theory, local fields, and Dedekind domains...

more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives...

infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important...

algebraic group. If the field k {\displaystyle k} is a local field (for instance the real or complex numbers, or a p-adic field) and G {\displaystyle \mathrm...

to allow a multipole expansion. The nearby charges then give rise to local field effects. In a common model of this type, the distant charges are treated...

global field is one of two types of fields (the other one is local fields) that are characterized using valuations. There are two kinds of global fields: Algebraic...

Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework...

momentum transfer to the spacecraft from some external source such as a local force field, which in turn must obtain it from still other momentum and/or energy...

when can local solutions be joined to form a global solution? One can ask this for other rings or fields: integers, for instance, or number fields. For number...

the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of...

algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies commutative local rings and...

counterterrorism field operations organized into squads, the number of which varies according to the amount and diversity of activity in the local field office's...

quasi-finite field is a generalisation of a finite field. Standard local class field theory usually deals with complete valued fields whose residue field is finite...

Let K be a non-Archimedean local field, meaning that K is complete under a discrete valuation with finite residue field. Then Br(K) is isomorphic to...

not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where R {\displaystyle R} is a commutative local ring. The...