- Function field
For function field in
algebraic geometry , see*
Function field of an algebraic variety
*Function field (scheme theory) A particular class is included under
global field .
Wikimedia Foundation. 2010.
Function field
Look at other dictionaries:
Function field of an algebraic variety — In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V . In complex algebraic geometry these are meromorphic functions and their higher dimensional analogues; in… … Wikipedia
Function field (scheme theory) — In algebraic geometry, the function field KX of a scheme X is a generalization of the notion of a sheaf of rational functions on a variety. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on … 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
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 of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… … Wikipedia
Field with one element — In mathematics, the field with one element is a suggestive name for an object that should exist: many objects in math have properties analogous to objects over a field with q elements, where q = 1, and the analogy between number fields and… … Wikipedia
Field emission — (FE) is the emission of electrons from the surface of a condensed phase into another phase due to the presence of high electric fields. In this phenomenon, electrons with energies below the Fermi level tunnel through the potential barrier at the… … Wikipedia
field — field, domain, province, sphere, territory, bailiwick are comparable when they denote the limits in which a person, an institution, or a department of knowledge, of art, or of human endeavor appropriately or necessarily confines his or its… … New Dictionary of Synonyms
function — n 1 Function, office, duty, province are comparable when they mean the act, acts, activities, or operations expected of a person or thing by virtue of his or its nature, structure, status, or position. Function is the most comprehensive of these… … New Dictionary of Synonyms
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
