In mathematics, a 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:[1]
Algebraic number field: A finite extension of
Global function field: The function field of an irreducible algebraic curve over a finite field, equivalently, a finite extension of , the field of rational functions in one variable over the finite field with elements.
An axiomatic characterization of these fields via valuation theory was given by Emil Artin and George Whaples in the 1940s.[2][3]
a globalfield 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:...
local and globalfields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However,...
mathematics, the adele ring of a globalfield (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic...
technique for constructing Galois groups of local fields using global Galois groups. A basic example of a field extension with an infinite group of automorphisms...
the field, described globalization as "the compression of the world and the intensification of the consciousness of the world as a whole." In Global Transformations...
is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long line of more concrete...
Global politics, also known as world politics, names both the discipline that studies the political and economic patterns of the world and the field that...
In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system...
joined to form a global solution? One can ask this for other rings or fields: integers, for instance, or number fields. For number fields, rather than reals...
mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...
in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety X over a globalfield, which measures...
as the World Service Authority, have advocated global transnational citizenship. The field of global citizenship, as a form of transnationality is transnationalism...
applications. Services The Services business includes three divisions: GlobalField Services, Energy and Sustainability Services, and Smart grid Services...
The magnetic field of Mars is the magnetic field generated from Mars's interior. Today, Mars does not have a global magnetic field. However, Mars did...
describes the abelianization of the Galois group of a local or globalfield, geometric class field theory describes the abelianized fundamental group of higher...
The Global Partnership on Artificial Intelligence (GPAI, pronounced "gee-pay") is an international initiative established to guide the responsible development...
The Bombardier Global Express is a large cabin, long-range business jet designed and manufactured by Bombardier Aviation. Announced in October 1991, it...
Enel X Global Retail is the Enel Group's global business line operating in the field of energy supply, energy management services, and public and private...
Q/Z, the Hasse invariant. The case of a globalfield K (such as a number field) is addressed by global class field theory. If D is a central simple algebra...
and 12,000 years. Although there have been periods in which the field reversed globally (such as the Laschamp excursion) for several hundred years, these...
Global Wind Day or World Wind Day is a worldwide event that is held on June 15. It is organised by WindEurope and GWEC (Global Wind Energy Council). It...
field Real closed fieldGlobalfield A number field or a function field of one variable over a finite field. Local field A completion of some global field...
Global Information
