Weak-⊕-locally artinian supplemented modules

In this study, it is defined the classes of (D_1LA)-modules, finitely generated (D_1WLA)-modules, ⊕_WLA-supplemented modules, (D_1GLA)-modules and given key features of these modules. It was shown that a (D_1LA)-module is a ⊕_WLA-supplemented module. It was shown that the finite direct sum of ⊕_WLA-supplemented modules is a ⊕_WLA-supplemented module. It has been proven that the direct sum of the ⊕_WLA-supplemented module satisfyıhg the condition (D_3) is also ⊕_WLA-supplemeted. It was obtained that every (D_1GLA)-module is a ⊕_WLA-supplemented module. It was also determined that if each locally artinian submodule of a locally artinian supplemented module can be lies above a direct summand, the module is ⊕_WLA-supplemented.