AAR8

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(Dis)prove: {\mathbb  {Z}}/(p)\times {\mathbb  {Z}}/(p)\cong {\mathbb  {Z}}/(p^{2})\, as rings, where p\, is prime.

This is false because {\mathbb  {Z}}/(p^{2})\, has a zero divisor p\cdot p=0 but {\mathbb  {Z}}/(p)\times {\mathbb  {Z}}/(p)\, doesn't because p\, is prime.


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