In the subfield of
algebra named
field theory, a
separable extension is an
algebraic field extension such that for every
, the
minimal polynomial of
over
F is a
separable polynomial (i.e., has distinct
roots; see below for the definition in this context). Otherwise, the extension is called
inseparable. There are other equivalent definitions of the notion of a separable algebraic extension, and these are outlined later in the article.