Uniserial rings (Q1078294)

R is an associative ring with 1, all R-modules are assumed to be unital. Let M be a right R-module and \(S=End M\) the endomorphism ring of M. If M is S-projective, then M is called an endoprojective right R-module. The author shows that a semisimple ring R, over which each injective right module is endoprojective, is Artinian. He then describes the rings R, such that each right R-module (resp. each quasi-injective right R-module) is endoprojective. It turns out that these rings R are primarily decomposable Artinian semichain rings in the terminology of \textit{C. Faith} [Algebra: Rings, modules and categories (1973; Zbl 0266.16001)].