TY - JOUR
T1 - Co-Commuting Mappings of Generalized Matrix Algebras
AU - Liang , Xinfeng
AU - Xiao , Zhankui
JO - Communications in Mathematical Research 
VL - 4
SP - 311
EP - 319
PY - 2021
DA - 2021/05
SN - 31
DO - http://doi.org/10.13447/j.1674-5647.2015.04.03
UR - https://global-sci.org/intro/article_detail/cmr/18913.html
KW - co-commuting map, generalized matrix algebra, proper.
AB - <p style="text-align: justify;">Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring&nbsp;$\mathcal{R}$&nbsp;and $Z(\mathcal{G})$ be the center of $\mathcal{G}$. Suppose that $F, T : \mathcal{G}&nbsp;→&nbsp;\mathcal{G}$ are two co-commuting $\mathcal{R}$-linear
mappings, i.e., $F(x)x = xT(x)$ for all $x ∈ \mathcal{G}$. In this note, we study the question of
when co-commuting mappings on $\mathcal{G}$ are proper.</p>