Q-soft R-Submodules and their properties

The purpose of this paper is to define the concept of Q-soft R- submodules over commutative rings and discuss their relationship with R- submodules. Next, We describe some of the their basic preoperties and discuss the master properties of them. Later, we introduce the concepts of sum, intersection and external direct sum of them and study some types of separation axioms of them. Finally, we investigate them under homomorphisms of R- submodules.