- Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 22 Issue: 6
- Extending property on EC-Fully Submodules
Extending property on EC-Fully Submodules
Authors : Ramazan Yaşar, Adnan Tercan
Pages : 1799-1803
Doi:10.16984/saufenbilder.420612
View : 14 | Download : 10
Publication Date : 2018-12-01
Article Type : Other
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