ℐ⨁ss−Supplemented modules

Abstract

We describe ℐss⨁ − supplemented modules as a proper generalisation of ⨁ss −supplemented modules. We show that each direct summand of a ℐss⨁ −supplemented module satisfying condition (D3) is also ℐss⨁ −supplemented. Then we prove that the finite direct sum of ℐss⨁ − supplemented submodules as a duo module is ℐss⨁ − supplemented. Moreover, we have given some types of rings whose modules are ℐss⨁−supplemented.