@article{article_585727, title={SS-supplemented modules}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={69}, pages={473–485}, year={2020}, DOI={10.31801/cfsuasmas.585727}, author={Kaynar, Engin and Türkmen, Ergül and Çalışıcı, Hamza}, keywords={strongly local module,semisimple module,ss-supplemented module}, abstract={<div>A module M is called ss-supplemented if every submodule U of M has a </div> <div>supplement V in M such that U(intersection)  V is semisimple. It is shown that a finitely generated </div> <div>module M is ss-supplemented if and only if it is supplemented and Rad(M) (submodule) Soc(M). A module </div> <div>M is called strongly local if it is local and Rad(M) (submodule)  Soc(M). Any direct sum of strongly </div> <div>local modules is ss-supplemented and coatomic. A ring R is semiperfect and Rad(R) (submodule) </div> <div>Soc( <sub>R </sub>R) if and only if  every left R-module is ss-supplemented if and only if <sub>R </sub>R is a finite sum of strongly local </div> <div>submodules. </div>}, number={1}, publisher={Ankara University}