Abstract
The paper focuses on neutrosophic algebraic structures and operations applicability to the study of classical al-gebraic structures, particularly the R-module. The definition of neutrosophic submodules P and Q was further developed upon in this work in order to create neutrosophic submodules of P + Q. In this study, the neutrosophic submodule of the direct sum M ⊕ N is constructed, analyzed, and its associated results are examined. Additionally, several algebraic results of the neutrosophic submodule’s direct sum of a non-empty arbitrary family of submodules are examined.
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