Suppose we have a commutative ring with identity, say $R$, and two proper ideals $I$ and $J$ s.t. :
$$IJ=I\cap J$$
I need to find an example of this situation where such ideals are not comaximals i.e. $I+J$ is properly contained in $R$.
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https://math.stackexchange.com/questions/290229/explaining-the-product-of-two-ideals I think that Martin Brandenburg's answer provides some example – 1123581321 Sep 29 '18 at 20:11
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4In $R = k[x,y]$, take $I= xR$ and $J = yR$. – Youngsu Sep 29 '18 at 22:08