On characterization of tripotent matrices in triangular matrix rings

Abstract

Let R be a ring with identity 1 whose tripotents are only −1, 0, and 1. It is characterized the structure of tripotents in T (R) which is the ring of triangular matrices over R. In addition, when R is finite, it is given number of the tripotents in Tn(R) which is the ring of n × n dimensional triangular matrices over R with n being a positive integer.