Show that if R has no zero divisors then R[x] also has no zero divisors.
Thinking about this problem ...
But cannot equal zero since all of the since R has no zero divisors
Thus R[x] has no zero divisors
Can someone please confirm that this solution is OK?
ck is a sum of elements, so there is no reason to suppose it can't be 0, even if all the terms in the sum are non-zero.
however, you're close...
cm+n = ambn ≠ 0, since am ≠ 0, and bn ≠ 0.
since this is the leading coefficient of f(x)g(x), f(x)g(x) cannot be the 0-polynomial.