On CS-modules over Goldie rings. (Q1433554)

CS-modules, i.e. modules in which every closed submodule is a direct summand, and their structure have been studied extensively since the middle 1980s. This paper takes the study further by investigating the structure of nonsingular CS-modules over a ring with finite right uniform dimension and of CS-modules over semiprime or prime right Goldie rings. For rings with finite uniform dimension, it is proven that a module over a nonsingular ring is a CS-module if and only if it is a 1-CS-module and every local summand is a summand. It is shown that the study of nonsingular modules over a semiprime right Goldie ring can be reduced to the study of modules which contain no nontrivial injective submodules. Characterizations of all nonsingular CS-modules over a semiprime right Goldie ring as well as of CS-modules over a prime right Goldie ring are found.