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 ,

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- December 11th 2012, 03:10 AMxinglongdadaMultiple root
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 , - December 11th 2012, 01:04 PMDrexel28Re: Multiple root
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.