field K is called a non-Archimedean local field if it is complete with respect to a metric induced by a discrete valuation v and if its residue field...

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...

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...

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

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...

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 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...

Field electron emission, also known as field-induced electron emission, field emission (FE) and electron field emission, is the emission of electrons from...

automorphic forms and representation theory of algebraic groups over local fields and adeles. It was described by Edward Frenkel as the "grand unified...

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...

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

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

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...

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...

In the mathematical field of Galois cohomology, the local Euler characteristic formula is a result due to John Tate that computes the Euler characteristic...

be local, or it might be nonlocal. Noether fields are often composite fields and they are local. In the generalized LSZ formalism, composite fields, which...

algebra, a locally compact field is a topological field whose topology forms a locally compact Hausdorff space. These kinds of fields were originally introduced...

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

axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are...

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...

to the group ring (Z/2Z)[F*/F*2] if q ≡ 1 mod 4. The Witt ring of a local field with maximal ideal of norm congruent to 1 modulo 4 is isomorphic to the...

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...

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...

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...

theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according...

MRI, the local field δ B {\displaystyle \delta B} induced by non-ferromagnetic biomaterial susceptibility along the main polarization B0 field is the convolution...

Formally real field Real closed field Global field A number field or a function field of one variable over a finite field. Local field A completion of...