arXiv subjects
Publications and source records attributed to Mikhail Chebotar.
Let $δ$ be a derivation of a locally nilpotent ring $R$. Then the differential polynomial ring $R[X; δ]$ cannot be mapped onto a ring with a non-zero idempotent. This answers a recent question by Greenfeld, Smoktunowicz and Ziembowski.
We prove that the ring of polynomials in several commuting indeterminates over a nil ring cannot be homomorphically mapped onto a ring with identity, i.e. it is Brown-McCoy radical. It answers a question posed by Puczylowski and Smoktunowicz. We also show that the central closure of a prime nil ring cannot be a simple ring with identity solving a problem due to Beidar.