On direct sums of uniform modules

Abstract EN

This paper studies direct sums of uniform modules.

We give a number of necessary and sufficient conditions for such a sum to complement uniform summands, or to have that local summands, of uniform submodules, are summands.

We also investigate direct sums of nonsingular uniform modules over semiprime right Goldie rings; and prove that if every finite subsum is a CS- module, then every closed submodule is a direct summand.

As a result, we show that the relative injectivity of every two distinct submodules appear in such a sum, is equivalent to the quasi-continuity