Extending property on EC-Fully Submodules

Year 2018, Volume: 22 Issue: 6, 1799 - 1803, 01.12.2018

Ramazan Yaşar , Adnan Tercan

https://doi.org/10.16984/saufenbilder.420612

Abstract

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.

Keywords

fully invariant, ec-fully submodule, FI-extending, extending, extending

References

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