SS-supplemented modules
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Tarih
2020-06-30Yazar
Kaynar, Ali
Türkmen, Ergül
Çalışıcı, Hamza
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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(RR) if and only if every left R-module is ss-supplemented if and only if RR is a finite sum of strongly local
submodules.