Formal triangular matrix ring with nil clean index $4$

Abstract

For an element $a\in R$, let $η(a)=\{e\in R\mid e^2=e\mbox{ and }a-e\in \mbox{nil}(R)\}$. 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 $\left(\begin{array}{ccc}A& M0& B\end{array}\right)$ with nil clean index $4$.

5 pages