⊕-s-extending module

الملخص EN

The concept⊕-s-extending modules will be purpose of this research, a module M is ⊕-s-extending if each submodule in M is essential in submodule has a supplement that is direct summand.

Initially, we give relation between this concept with weakly supplement extending modules and ⊕-supplemented modules.

In fact, we give the following implications: Lifting modules ⟹ ⊕-supplemented modules ⟹ ⊕-s-extending modules ⟹ weakly supplement extending modules.

It is also we give examples show that, the converse of this result is not true.

Moreover, we study when the converse of this result is true.