NILPOTENT an‎d LINEAR COMBINATION OF IDEMPOTENT MATRICES

A ring R is Zhou nil-clean if every element in R is the sum of a nilpotent and two tripotents. Let R be a Zhou nil-clean ring. If R is of bounded index or 2-primal, we prove that every square matrix over R is the sum of a nilpotent and a linear combination of two idempotents. This provides a large class of rings over which every square matrix has such decompositions by nilpotent and linear combination of idempotent matrices