A First Course in Abstract Algebra Chapter S.22, Problem 27E
Let F be a field of
characteristic zero and let D be
the formal polynomial differentiation map, so
that. D(a0 + a1x + a2x^2 + ••• + anx^n) = a1 + 2 • a2x + •••+n•
anxn-1, i.e.
F be a field of characteristic zero , D:F[x]→F[x].
C) Find the image of F[x] under D. Is it important which
characteristic the field has? Can you explain this enough?
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