Let $R$ the polynomial ring in $n$ variables with complex coefficients and $I$ an ideal of $R$. Is it true that if $R/I$ is CM also $R/J$ is CM (where $J$ is the radical of $I$)?
Is there a relations between a resolution of $R/J$ and one of $R/I$? What if I suppose that $proj.dim(R/I)=2$?



CM for radical ideal
It is [not true](http://www.uni-due.de/~mat306/preprints/radical.pdf), but the example is not easy to find $I = (x\_2^2-x\_4x\_5,x\_1x\_3-x\_3x\_4, x\_3x\_4-x\_1x\_5)$! 


