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

Area of Science:

• Abstract Algebra
• Module Theory

Background:

• Focuses on unitary modules and commutative rings with identity.
• Explores connections between different types of modules within abstract algebra.

Purpose of the Study:

• Define and investigate a new class of modules: S-pseudo bounded F-modules.
• Establish relationships between S-pseudo bounded modules and other established module types.
• Introduce novel conditions and properties for these modules.

Main Methods:

• Definition of S-pseudo bounded F-modules.
• Utilizing F-homomorphisms and endomorphisms of F-modules.
• Exploring connections through the set of endomorphisms, End(M).

Main Results:

• Introduced S-pseudo bounded F-modules (S-PS.B. F-modules).
• Established links between S-pseudo bounded modules and monoform, quasi-Dedekind, compressible, and retractable modules.
• Demonstrated how S-pseudo bounded modules yield other module types, including retractable and injective modules.

Conclusions:

• The study successfully defined S-pseudo bounded modules and explored their properties.
• New conditions and interconnections with other module classes were established.
• The research contributes to the understanding of module theory by introducing a novel module classification.