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Given some ring $R$ and two ideals $I$ and $J$ of $R$ such that $I \neq J$, is it possible for $R/I \cong R/J$?

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    Am I missing something or does the example $I \times 0$ and $0 \times I$ in $R \times R$ already answer your question?2011-03-23
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    If you want an example for an integral domain then you can take $R=\mathbb{Z}[i]$, $I=(2+i)$, $J=(2-i)$.2011-03-23
  • 0
    Would there be certain conditions on the ideals and the ring in order for the quotients to be isomorphic?2011-03-23

2 Answers 2