The Rank of UV-Generated Modules

Let U be a nonempty set of R-modules and V be a submodule of ��U�, U� 2 U for all � 2 �. A UV generated module is a generalization of U-generated module by using the concept of V-coexact sequence. We say that an R-module N is generated by UV if there is an epimorphism from V to N. In this paper, we introduce the definition of rank of UV-generated modules. Furthermore, we investigate some properties of rank of UV-generated modules.