Simple continuous modules

Authors : Yongduo WANG

Pages : 1336-1344

View : 65 | Download : 6

Publication Date : 2019-10-08

Article Type : Research Paper

Abstract :A module $M$ is called a simple continuous module if it satisfies the conditions $insert ignore into journalissuearticles values(min-C_{1});$ and $insert ignore into journalissuearticles values(min-C_{2});$. A module $M$ is called singular simple-direct-injective if for any singular simple submodules $A$, $B$ of $M$ with $A\cong B\mid M$, then $A\mid M$. Various basic properties of these modules are proved, and some well-studied rings are characterized using simple continuous modules and singular simple-direct-injective modules. For instance, it is shown that a ring $R$ is a right $V$-ring if and only if every right $R$-module is a simple continuous modules, and that a regular ring $R$ is a right $GV$-ring if and only if every cyclic right $R$-module is a singular simple-direct-injective module.
Keywords : simple continuous module, singular simple direct injective module, V ring, GV ring

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