Jordan C Bounds

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20182025

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math.RA2025

Commuting maps on the Heisenberg algebra

Jordan Bounds, Ellis Edinkrah

Given a ring $R$ with center $Z (R)$ , we say a linear map $f : R \to R$ is commuting if $[f (x), x] = 0$ for all $x \in R$ . Such a map has a standard form if there exists $λ \in R$ a…

math.RA2025

Bilinear maps on the ring of strictly upper triangular matrices

Jordan Bounds, Samuel Dayton, Regan Richardson +1

Let $R$ be a 2-torsion free unital ring and $N_{n} = N_{n} (R)$ the ring of strictly upper triangular matrices with entries in $R$ and center $Z = Z (N_{n})$ . It has been previously shown that…

math.RA2023

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

Jordan Bounds

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 commutin…