I just want to check whether my solutions are right. The rings are $$\mathbb{Z}_{75}\text{ and } \frac{\mathbb{Q}[x]}{((x-2)^2)}$$ The first one is finite so it is Artinian and the second is a finite dimensional algebra over an Artinian ring, so it is Artinian. For the composition series, I picked $$0<(25)<(5)< \mathbb{Z}_{75}$$ and $$0< \frac{(x-2)}{((x-2)^2)}< \frac{\mathbb{Q}[x]}{((x-2)^2)}$$ Am I wrong?
2026-03-25 17:24:54.1774459494
Are these rings Artinian? Are the composition series correct?
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