I’m studying rings of polynomials And I don’t understand the following exercise.
“Let F be a field and char(F)=0
Let D : F[x] -> F[x] defined by D(f(x))=f’(x)
Find image of F[x] under D”
The solution says antiderivatives of f’(x) are in F[x], so D is surjective.
But I don’t understand what $\frac{1}{n+1}$$a_ n x^{n+1}$ means.
Is it in F[x]??
I know n$a_n$ = $\sum_{i=1}^n a_n$ but what about $\frac{1}{n+1} a_n$??
When k is an element of a field F, what is $\frac{1}{n} k$ ?
Thank you