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Exercise 7.3.12

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Suppose, for the sake of contradiction, there is a polynomial $g (t)$ of degree $n$ such $g (D) = T_{0}$ . Then we know that $g (D) (x^{n})$ is a constant but not zero. This is a contradiction to the fact $g (D) (x^{n}) = T_{0} (x^{n}) = 0$ . So $D$ has no minimal polynomial.

jephianlin

2011-06-27 00:00

Exercise 7.3.12

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