field extension

Hello, you have come here looking for the meaning of the word field extension. In DICTIOUS you will not only get to know all the dictionary meanings for the word field extension, but we will also tell you about its etymology, its characteristics and you will know how to say field extension in singular and plural. Everything you need to know about the word field extension you have here. The definition of the word field extension will help you to be more precise and correct when speaking or writing your texts. Knowing the definition offield extension, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.

English

English Wikipedia has an article on:
Wikipedia

Noun

field extension (plural field extensions)

  1. (algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L.
    • 1974, Thomas W. Hungerford, Algebra, Springer, page 230:
      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).
    • 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 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.

Usage notes

Hyponyms

Meronyms

Translations

Further reading

Anagrams