Let given ring $R$ and subring $R_0\leq R$, let $p$ is prime number, such that $\forall r\in R, \exists i>0 : p^ir\in R_0$. Is it true that if $Nil(R_0/pR_0)=\{0\}$, then $Nil(R/pR) =\{0\}$?
Subring of ring
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