Abstract:
The weakly regularity of all right $R$-modules with $R$ an arbitrary ring does not imply the same property of all left $R$-modules. We describe the rings over which every right and left module is weakly regular and also obtain some description of semiartinian $CSL$-rings.
Keywords:weakly regular module, quasiprojective module, semiartinian ring $SV$-ring, $CSL$-ring.