@article{article_1213444, title={A note on CSP rings}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={52}, pages={1022–1028}, year={2023}, DOI={10.15672/hujms.1213444}, author={Ma, Haitao and Shen, Liang}, keywords={CSP rings, CS rings, SSP rings, self-injective rings, regular rings}, abstract={A ring $R$ is called right CSP if the sum of any two closed right ideals of $R$ is also a closed right ideal of $R$. Left CSP rings can be defined similarly. An example is given to show that a left CSP ring may not be right CSP. It is shown that a matrix ring over a right CSP ring may not be right CSP. It is proved that $\mathbb{M}_{2}(R)$ is right CSP if and only if $R$ is right self-injective and von Neumann regular. The equivalent characterization is given for the trivial extension $R\propto R$ of $R$ to be right CSP.}, number={4}, publisher={Hacettepe University}, organization={NSFC}