On Modules with Finite Goldie Dimension

It is proved that (i) if R is a ring with unity and having finite dimension then for an unitary R-module M the conditions: (a) M has finite Goldie dimension and descending chain condition on essential submodules, and (b) M is finitely embedded and M/Scyc (Ai) has descending chain condition on its submodules, are equivalent, and (ii) if every quotient submodule of the R-module R has finite Goldie dimension and the R-module R has descending chain condition on its essential submodules then every R module is either finitely embedded or infinitely embedded.