Volume 25 β’ Issue 4 β’ PP: 316-321 β’ 2025
On Modules Related to Homomorphism Their Kernel Equal Zero in Neutrosophic Theory
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Neutrosophic set is a modern branch as a generalization of fuzzy concept. Zadeh in 1965 presented fuzzy concept and later he introduced more applications in more subjects of mathematics. On of the type branch of mathematics is fuzzy algebra. In this work, we present and clarify several results of several modules, which has zero-kernel, and zero homomorphism in neutrosophic theory. The aim modules are mnonoform and small monoform modules. Several concepts have been studied in this paper like Quasi-dedekind and uniform modules. We proved that if ( ( )) is a module over neutrosophic ring ( ). If ) is a directed sum of simple submodules an is monoform, then ) is monoform module. Also, if π―) is a semi simple ring and π―) is a π―)-module, so π―) is small and satisfies all conditions of monoform with Q-dedekind property. On the other hand, let be an R-module. is a neutrosophic modules and generated by and . So, is a weak neutrosophic. Finally, we presented more results, examples and properties about the topic with new results in neutrosophic algebra.
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