Fourteen years ago: Ad-nilpotent ring? Quasi-algebra?
Facebook entry dated August 8, 2011 -- https://www.facebook.com/posic/posts/pfbid02fV6jhkzDhcoSGFvWBYxfJ3BBtJMFuZqD5xKNSBQ43a4EZVzJUrxfz1LBmJWp52ALl :

"How does one call a noncommutative ring that is a differential bimodule over its (fixed) commutative subring (like the differential operators over the functions)? The term "differential algebra" means something entirely different, of course. Ad-nilpotent ring? Quasi-algebra?"

A longer LJ entry in Russian -- https://posic.livejournal.com/644354.html

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Fourteen years have passed. I started working at HSE and quit working at HSE, moved to Israel, then moved to Prague. Changed positions, grants, etc. I have lived through the idiotic Covid panic, I have seen several catastrophic wars being started in quick succession, etc.

But I have not forgotten about my quasi-algebras. I am typing a long treatise on quasi-algebras. Most of it is on the arXiv already. I have also written a separate paper on quasi-modules (a.k.a. differential bimodules).

And quasi-algebras are not even similar to contramodules, as far as my "career" is concerned. I have not invented quasi-algebras; I cannot conceivably become famous for studying them. Differential bimodules have been known since early 1990s if not before. Still I am being faithful to my ideas about quasi-algebras. I am developing them.