Volume 31, Issue 4
Co-Commuting Mappings of Generalized Matrix Algebras

Commun. Math. Res., 31 (2015), pp. 311-319.

Published online: 2021-05

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• Abstract

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.

• Keywords

co-commuting map, generalized matrix algebra, proper.

16W20, 15A78, 47L35

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@Article{CMR-31-311, author = {Xinfeng and Liang and and 18694 and and Xinfeng Liang and Zhankui and Xiao and and 18695 and and Zhankui Xiao}, title = {Co-Commuting Mappings of Generalized Matrix Algebras}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {311--319}, abstract = {

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} }
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 -

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.

Xinfeng Liang & Zhankui Xiao. (2021). Co-Commuting Mappings of Generalized Matrix Algebras. Communications in Mathematical Research . 31 (4). 311-319. doi:10.13447/j.1674-5647.2015.04.03
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