field extension

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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.

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