Suppose that is a finite dimensional vector space over . Let for some liner .

Then:

a) If is a ploynomial over F, show that .

b) Show that

c) Show that is the LCM of and thus a product of them if they are pairwise coprime.

d) Suppose theyarepairwise coprime. Show that

I've got a). I just let be a general poly, and kind of multiplies everything out, rearranged a bit.

I think c) follows almost directly from b), but I don't know how to show b) or d).