Authors: TUĞBA PETİK

Abstract: Let $\mathfrak{R}$ be a ring with identity $1$ whose tripotents are only $-1$, $0$, and $1$. It is characterized the structure of tripotents in $\mathcal{T}(\mathfrak{R})$ which is the ring of triangular matrices over $\mathfrak{R}$. In addition, when $\mathfrak{R}$ is finite, it is given number of the tripotents in $\mathcal{T}_{n}( \mathfrak{R})$ which is the ring of $n\times n$ dimensional triangular matrices over $\mathfrak{R}$ with $n$ being a positive integer.

Keywords: Tripotent matrix, triangular matrix, matrix rings

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