Extending property on EC-Fully Submodules

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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Volume: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 : 21 | Download : 9

Publication Date : 2018-12-01

Article Type : Research Paper

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

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