• Honam Mathematical Journal
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• v.42 no.2
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• pp.293-300
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• 2020

In this article, we define a (an amply) F_δ-supplemented module in category of R-Mod. The general properties of F_δ-supplemented modules are briefly discussed. Then, concentrating on the F_δ-small submodule, we find the necessary and sufficient condition for F_δ- supplemented modules. Also, we introduce ascending chain condition for F_δ-small submodules of any module and establish a basic theorem for amply F_δ-supplemented modules by using π-projectivity.