Let be an arbitrary field, while is the complex field. is a polynomial in with degree . Suppose has no multiple factor in , prove then has no multiple root in
Here, we mean by is a multiple factor of , if is irreducible, and for some ,
This doesn't make any sense as written? I'm going to assume that is a subfield of . Recall then that having no multiple roots is equivalent to , which is trivially independent of what field you are discussing. Once again, this question dreally doesn't make sense.