  In this paper we will study $k$-commuting mappings of generalized matrix
algebras. The general form of arbitrary $k$-commuting mapping of a generalized
matrix algebra is determined. It is shown that under mild assumptions, every
$k$-commuting mapping of a generalized matrix algebra takes a certain form
which is said to be proper. A number of applications related to $k$-commuting
mappings are presented. These results extend the existing works of Cheung, Du
and Wang \cite{Cheung2, DuWang1} to the case of generalized matrix

Rings and Algebras