A characterization of Goldie extending trivial Morita contexts.

A module M is said to be extending (Goldie extending) if for each submodule X ≤ M , there exists a direct summand D of M such that X is essential in D (if for every submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D). In this paper, a necessary and sufficient condition is obtained for a trivial Morita context ring to be right Goldie-extending. [ABSTRACT FROM AUTHOR]