Dictionary

field extension en · NOUN

Meanings

1. (qualifier:field theory) Any pair of fields, denoted L/K, such that K is a subfield of L.
   • A Galois field extension may be defined in terms of its Galois group (Section 2) or in terms of the internal structure of the extension (Section 3). 1974, Thomas W. Hungerford, Algebra, Springer, page 230:
   • 1998, David Goss, Basic Structures of Function Field Arithmetic, Springer, Corrected 2nd Printing, page 283, Note that the extension of L obtained by adjoining all division points of ψ includes at most a finite constant field extension.
   • 2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2bd Edition, page 530, A field extension of a field K is, in particular, a K-algebra. Hence any two field extensions of K have a tensor product that is a K-algebra.

Forms

Hyponyms

simple extension · algebraic extension · transcendental extension · trivial extension

Meronyms

base field · extension field

Relateds

extension field · extension

Translations (3)

pl rozszerzenie ciała (pair of fields such that one is a subfield of the other) · bg разширение (pair of fields such that one is a subfield of the other) · fi kuntalaajennus (pair of fields such that one is a subfield of the other)