Power commuting and centralizing maps on the ring of strictly upper triangular matrices

Jordan Bounds

paper

Power commuting and centralizing maps on the ring of strictly upper triangular matrices

arXiv:2301.03422

Abstract

Let $N_{n} (F)$ denote the ring of strictly upper triangular matrices with entries in a field $F$ of characteristic zero and center $Z (N_{n} (F))$ . We characterize the $2$ -power commuting maps over $N_{n} (F)$ , maps satisfying the identity $[f (X), X^{2}] = 0$ for all $X \in N_{n} (F)$ . As a consequence, we also obtain a characterization of the maps centralizing maps over $N_{n} (F)$ , maps satisfying $[f (X), X] \in Z (N_{n} (F))$ for all $X \in N_{n} (F)$ .