(untitled) (Communications in Mathematical Research, 2021)
Let G be a generalized matrix algebra over a commutative ring R and Z(G) be the center of G. Suppose that F, T : G → G are two co-commuting R-linear mappings, i.e., F(x)x = xT(x) for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.