# Locally nilpotent derivations on rings with zero divisors

Almost all books that I have found deal with derivation on several types of rings (or algebras) (for instance, commutative, noncommutative, domains, non-domains etc).

However, each paper about locally nilpotent derivations (that I know) suppose the ring is a domain.

Question: what happens with rings containing zero divisors and the study of locally nilpotent derivations? Does exist any phenomenon on them?

I appreciate any reference.

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Yes: Jeffrey Bergen and Piotr Grzeszczuk have co-authored a few papers on skew polynomial rings $$R[x;\sigma,\delta]$$ and skew power series rings $$R[[x;\sigma,\delta]]$$ where $$\delta$$ is locally nilpotent. They don't always assume $$R$$ is a domain: sometimes they simply require $$R$$ to contain a field. Here are the first few papers of theirs that I'm familiar with: