field extension

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an extension field of the real numbers, and the real numbers are an extension field of the rational numbers. The extension field degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e., [K:F] = dim_F K.

class group | class number | extension field degree | extension ring | field | field automorphism | Galois theory | Pythagorean extension | splitting field | subfield