There
are several generalizations of -modules
in literature. One of the generalization is based on fully invariant
submodules. Recall that a
module is called -extending
if every fully invariant submodule is essential in a direct summand. We call a module
-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 -extending
modules is -extending.
Again, like the -extending
property, the -extending
property is shown to carry over to matrix rings.
Primary Language | English |
---|---|
Subjects | Mathematical Sciences |
Journal Section | Research Articles |
Authors | |
Publication Date | December 1, 2018 |
Submission Date | May 3, 2018 |
Acceptance Date | June 26, 2018 |
Published in Issue | Year 2018 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.