On F-Supplemented Modules

Let R be a ring and M a right R–module. In this paper we prove that if M is weakly F-supplemented, then every factor module and every F-coclosed submodule of M is again weakly F-supplemented. In [5], it is shown that Rad(M) has finite uniform dimension iff M does not contain an infinite direct sum of nonzero small submodules. Here we replace F-small submodules instead of small submodules (which is a weaker condition) and obtain the same result; i.e, we show that if M does not contain an infinite direct sum of F-small submodules, then Rad (M) has finite uniform dimension.