Formal triangular matrix ring with nil clean index $4$

Abstract: For an element $a \in R$, let $\eta(a)={e\in R\mid e^2=e\mbox{ and }a-e\in \mbox{nil}(R)}$. The nil clean index of $R$, denoted by NinA$(R)$, is defined as Nin$(R)=\sup {\mid \eta(a)\mid: a\in R}$. In this article we have characterized formal triangular matrix ring $\begin{pmatrix}A & M0 & B\end{pmatrix}$ with nil clean index $4$.