Some general form of small submodules

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand.

10.22034/as.2026.23793.1836

Abstract

In this paper, we introduce and study the concept of $S$-$F$-small submodules, where $S$ is a multiplicatively closed subset of a ring $R$, and $F$ is a proper submodule of a right $R$-module $M$. This notion generalizes both $S$-small submodules and $F$-small submodules. Moreover, we establish conditions under which a right $R$-module $M$ is an $S$-$F$-small submodule. Finally, we present the relationships among $S$-essential submodules, $S$-small submodules, $S$-$D$-essential submodules, and $S$-$F$-small submodules under special conditions, where $D$ is a nonzero submodule of a right $R$-module $M$.

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 22 September 2026

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