# an example of regular ring with nilpotent elements

A regular local ring is a domain. But in general, a regular ring is not domain, so you can find regular rings with nilpotent elements.

I am unable to construct an example of (A, I) as

A is a regular ring, I is a nilpotent ideal and A/I is regular

Any help would be appreciated

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However, a regular ring can contains zero-divisors. For example the ring $k[x]\times k[y]$, representing the disjoint union of two affine lines, is not a domain but regular.
And by the way, if $I$ is a nilpotent ideal, $A/I$ needs not contain nilpotent element, and in fact, it would have less nilpotent elements than $A$.