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Let $R$ be a finite commutative ring. Does $R$ must be a direct product of local rings? The basic example is $\mathbb Z/n\mathbb Z$, but I can not find any counter example. If the answer is no, then in what conditions $R$ is a direct product of local rings?

boaz
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    Yes, every Artinian commutative ring is a finite direct product of Artinian local rings (and every finite ring is Artinian): https://math.stackexchange.com/questions/3243164/every-artinian-ring-is-isomorphic-to-a-direct-product-of-artinian-local-rings – Qiaochu Yuan Nov 22 '20 at 07:31
  • Thanks @ Qiaochu Yuan ! – boaz Nov 22 '20 at 08:37

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