In this work, we introduce and study a new generalization of the class of extending modules namely rationally principally extending module (for shortly, RP-extending); and we give many properties with this type of generalizations. On the other hand, we present a new class of modules namely Rc-sub modules and Rc-modules. Several properties and characterizations of these notions are given. Also we study the relation with our notions and some related well known concepts. [ABSTRACT FROM AUTHOR]