- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 69 Issue: 1
- SS-supplemented modules
SS-supplemented modules
Authors : Engin Kaynar, Ergül Türkmen, Hamza Çalişici
Pages : 473-485
Doi:10.31801/cfsuasmas.585727
View : 14 | Download : 5
Publication Date : 2020-06-30
Article Type : Research
Abstract :A module M is called ss-supplemented if every submodule U of M has a supplement V in M such that U(intersection) V is semisimple. It is shown that a finitely generated module M is ss-supplemented if and only if it is supplemented and Rad(M) (submodule) Soc(M). A module M is called strongly local if it is local and Rad(M) (submodule) Soc(M). Any direct sum of strongly local modules is ss-supplemented and coatomic. A ring R is semiperfect and Rad(R) (submodule) Soc( R R) if and only if every left R-module is ss-supplemented if and only if R R is a finite sum of strongly local submodules.Keywords : strongly local module, semisimple module, ss-supplemented module