New Class of S-Pseudo Bounded Modules With Some Related Concepts

In the present study , every module $M$ is unitary and every ring $F$ is commutative with identity. We gave a definition of a new class $F-\text{module}$ which is namely S-pseudo bounded module symbolically (S-PS.B. $F-$ module) and introduced some different approaches to attach this class with other types of well-known modules such that monoform module, quasi-Dedekind module, compressible module and retractable module. The main purpose of this article is to present a few new conditions for some corollaries and properties. The $F-$ homomorphism of monoform and compressible modules connect in a useful way with an endomorphism of a $F-$ module $M$ that we relied on it in the definition of S-pseudo bounded module. We used the symbol $\mathrm{End}\left(M\right)$ which means the set of all endomorphism maps of $F-$ module $M$ . Also S-pseudo bounded module gave us directly or with some conditions different modules such as retractable module, an injective module and others.