Thread: separable extension and separable polynomial

If is a splitting field over of a separable polynomial, why is a separable extension of which means , is a root of a separable polynomial over ?

Originally Posted by ynj

If is a splitting field over of a separable polynomial, why is a separable extension of which means , is a root of a separable polynomial over ?

the proof of this theorem can be found in any textbook in field theory. the idea is to prove, by induction over that

Em..I am sorry that I do not fully understand whay my book is saying..but now I understand...