I'm not being able to check why are these two quotients equal.
$\mathbb C[x]/(x^2-x^3)= \mathbb C[x]/(x^2)$
Can someone tell me why is it valid?
2026-04-02 14:16:47.1775139407
Why are these two quotients equal?
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Hint
A multiplicative Ideal generated by a Polynomial $p(x)$ in $\mathbb C[x]$ is the set given by $$(p) = \{ f\in \mathbb C[x] : f(x) = 0 \Leftarrow p(x) = 0\}$$ Can you find a polynomial $f$ such that $f\in (x^2) \setminus (x^2-x^3)$? (Look at the factorings)
If $(p)\ne(q)$ then $\mathbb C[x]/(p) \ne \mathbb C[x]/(q)$.