In
abstract algebra, the
splitting field of
f in
E is the smallest
subfield[?] of
E containing
F and all the roots <math>\alpha_1</math>, <math>\alpha_n</math>, ..., <math>\alpha_n</math> of a
polynomial f of degree
n.
This is noted <math>F(\alpha_0, \alpha_2, ..., \alpha_n)</math>.