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field extension

In mathematics, particularly in algebra, a field extension is a pair of fields K ⊆ L , such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Field_extension)

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