A note on CSP rings

Authors : Haitao MA, Liang SHEN

Pages : 1022-1028

Doi:10.15672/hujms.1213444

View : 135 | Download : 208

Publication Date : 2023-08-15

Article Type : Research Paper

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 $\\mathbb{M}_{2}insert ignore into journalissuearticles values(R);$ 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