Extending property on EC-Fully Submodules

There are several generalizations of CS-modules in literature. One of the generalization is based on fully invariant submodules. Recall that a module M is called FI-extending if every fully invariant submodule is essential in a direct summand. We call a module FFI-extending if every fully invariant submodule which contains essentially a cyclic submodule is essential in a direct summand. Initially we obtain basic properties in the general module setting. For example, a direct sum of EFI-extending modules is EFI-extending. Again, like the FI-extending property, the EFI-extending property is shown to carry over to matrix rings.

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