SS-supplemented modules

Authors : Engin KAYNAR, Ergül TÜRKMEN, Hamza ÇALIŞICI

Pages : 473-485

Doi:10.31801/cfsuasmas.585727

View : 50 | Download : 17

Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :A module M is called ss-supplemented if every submodule U of M has a supplement V in M such that Uinsert ignore into journalissuearticles values(intersection);  V is semisimple. It is shown that a finitely generated module M is ss-supplemented if and only if it is supplemented and Radinsert ignore into journalissuearticles values(M); insert ignore into journalissuearticles values(submodule); Socinsert ignore into journalissuearticles values(M);. A module M is called strongly local if it is local and Radinsert ignore into journalissuearticles values(M); insert ignore into journalissuearticles values(submodule);  Socinsert ignore into journalissuearticles values(M);. Any direct sum of strongly local modules is ss-supplemented and coatomic. A ring R is semiperfect and Radinsert ignore into journalissuearticles values(R); insert ignore into journalissuearticles values(submodule); Socinsert ignore into journalissuearticles values( 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

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