Commun. Math. Res., 31 (2015), pp. 311-319.
Published online: 2021-05
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Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring $\mathcal{R}$ and $Z(\mathcal{G})$ be the center of $\mathcal{G}$. Suppose that $F, T : \mathcal{G} → \mathcal{G}$ 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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.03}, url = {http://global-sci.org/intro/article_detail/cmr/18913.html} }Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring $\mathcal{R}$ and $Z(\mathcal{G})$ be the center of $\mathcal{G}$. Suppose that $F, T : \mathcal{G} → \mathcal{G}$ 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.