Nilperiod rings are NI-rings

A ring $R$ is nilperiod if every nilpotent element of $R$ is eventually annihilated by a power map in the sense established in the paper, and it is an NI-ring if its set of nilpotent elements is an ideal, equivalently if $\operatorname{Nil}(R)=\operatorname{Nil}^*(R)$. Nilperiod-ring conjecture. Every nilperiod ring is an NI-ring. This would extend the preceding results on nilperiod rings, which establish the conclusion under additional hypotheses such as centrality and torsion of nilpotent elements; whether those hypotheses can be removed is the issue posed here.