A note on CSP rings

Year 2023, , 1022 - 1028, 15.08.2023

Haitao Ma , Liang Shen

https://doi.org/10.15672/hujms.1213444

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.

Keywords

CSP rings, CS rings, SSP rings, self-injective rings, regular rings

Supporting Institution

NSFC

Project Number

No.11871145 and No.12071070

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