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field extension

noun

Definitions

  1. 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).
    • 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.

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA