extension field

Noun

extension field (plural extension fields)

1. (field theory) A field L which contains a subfield K, called the base field, from which it is generated by adjoining extra elements.
   • Suppose F is a subfield of the field K. Then K is called an extension field of F. So, for instance, GF(4) and GF(8) are extension fields of GF(2), although GF(8) is not an extension field of GF(4).1992, James G. Oxley, “Matroid Theory”, in Paperback, Oxford University Press, published 2006, page 215
   • This extension field of F always contains a root of f in the sense that if K#61;F#91;x#93;#47;(f(x)) then x is a root of f(y) in K#91;y#93;. It then follows that any polynomial will have roots, either in the original field of its coefficients or in some extension field.1995, Terence Jackson, From Polynomials to Sums of Squares, Taylor & Francis, page 56

   Synonyms:

   extension