A Remark on Derivations and Bounded Nilpotence Index

Abstract

Pace P. Nielsen and Michal Ziembowski has constructed a nil ring $R$ which has bounded nilpotence index 2 and proved that this ring has a derivation $\delta $ for which the differential polynomial ring $R[x;\delta ]$ is not even prime radical and thus obtained some interesting algebraically important results. The purpose of this note is to establish that the ring $R$ constructed by these authors is nothing but an even square ring whose every element is a nil element.