Given some ring $R$ and two ideals $I$ and $J$ of $R$ such that $I \neq J$, is it possible for $R/I \cong R/J$?
uniqueness of quotient rings
4
$\begingroup$
ring-theory
-
1Am 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
-
2If 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
-
0Would there be certain conditions on the ideals and the ring in order for the quotients to be isomorphic? – 2011-03-23