DOI: 10.12688/f1000research.172188.3 ISSN: 2046-1402

S-Pseudo Bounded Radical of Submodules

Amal Madhi Rashid, Buthyna Najad Shihab
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In this paper, every module M is unitary and every ring F is commutative with identity.The paper studied properties of the S-pseudo bounded radical. We used the symbol End ( M ) which means the set of all endomorphism maps of F − module M and S − rad M PS . B . ( ℵ ) refers to the intersection of all S-pseudo bounded submodules of M containing ℵ. The characterization of S-Pseudo bounded radical for finitely generated and multiplication module is given. It must be emphasized that scalar module and prime submodule played a major role in achieving new results and to study the relationship between the radical of submodules and the radical of S-pseudo bounded submodule. In our work, many properties and corollaries were established, which illustrated the concept of the radical of an S-pseudo bounded submodule and a new class of F − modules , as well as F − submodules . Some examples were provided to demonstrate and clarify this type of module (submodule) in a clear and effective manner.

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