# Let D be the differentiation operator on P(R), the space of polynomials over R. Prove that there exists no polynomial g(t) for which g(D) = T0. Hence D has no minimal polynomial.

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Let D be the differentiation operator on P(R), the space of polynomials over R. Prove that there exists no polynomial g(t) for which g(D) = T0. Hence D has no minimal polynomial.

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Step 1

Let D be the differentiation operator on P(R), the space of polynomials over R.

To prove-  There exists no polynomial g(t) for which g(D) = T0.

Hence D has no minimal polynomial.

Step 2

Let us suppose in contradiction that a polynomial ( g(t ) ) of degree n.

Such that

Step 3

After differentiating it n times, the result is a non zero con...

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