Unified Isomorphism Theory for r-Neutrosophic G- Submodules

Abstract

Neutrosophy is a logical framework that treats uncertainty, truth and falsity as distinct concepts hence better representing ambiguous information. In this paper,  we analyze r-neutrosophic G-submodules, where r in  [0,1], that bring about the application of known neutrosophic ideas in a more constrained algebraic context. The concept of r-neutrosophic quotient submodules is introduced as an extension of this and some characteristics are recognized and explained. The paper then focuses on the isomorphism properties of r-neutrosophic G-submodules by analysing and proving a version of the isomorphism theorems modified to this limited setting. The results show that the fundamental characteristics of the general neutrosophic G-submodule isomorphism is preserved in this constrained form. This illustrates that r-neutrosophic G-submodules maintain the essential algebraic structure of the extensive framework.