Field extension
If and
are fields and
, then
is said to be a field extension. We sometimes say that
is a field extension of
.
If is a field extension, then
may be thought of as a vector space over
. The dimension of this vector space is called the degree of the extension, and is denoted by
.
Given three fields , then, if the degrees of the extensions
,
and
, are finite, then are related by the tower law:
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