In this paper, we will present a new result that clarify the relationship between divisible module and Injective module. But before starting to give the most important results, we need to present the following lemma with some basic definitions that help us reach the desired goal.
In this work, we study C1-(extending) module M through the sub-module of M which have two properties namely prime and semi-prime (P. (S. P)). Indeed these properties with another concept like fully invariant of any sub-modules explain the main objective of this study. Also heart submodule of a module M and the socle of M are studied with fully invariant property to obtain the same objective.
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