Field extension

In mathematics, and, particularly, in algebra, a field extension is a pair of fields E ⊆ F , {\displaystyle E\subseteq F,} such that the operations of E are those of F restricted to E. In this case, F is an extension field of E and E is a subfield of F. 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.

Words

This table shows the example usage of word lists for keywords extraction from the text above.

WordWord FrequencyNumber of ArticlesRelevance
extension5138310.24
subfield33590.232
e6667160.212
field6927450.196
f5448430.193

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