Journals Information
Mathematics and Statistics Vol. 13(5), pp. 337 - 344
DOI: 10.13189/ms.2025.130509
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Rough Injective G-Modules
S. Sangeetha 1, Shakeela Sathish 2,*, B. Muthu Deepika 1, B. Srirekha 1
1 Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, Tamil Nadu, India
2 Department of Computing Technologies, School of Computing, SRM Institute of Science and Technology, Karrankulathur, Tamilnadu, India
ABSTRACT
The concept of a G-module serves as a fundamental link between group theory and module theory, offering a powerful algebraic framework for analyzing group actions on modules. In this paper, we extend the classical theory of G-modules by incorporating the mathematical foundation of rough set theory, which is well-suited for modeling uncertainty, vagueness, and indiscernibility. To this end, we introduce and formalize the notion of rough G-modules鈥攁lgebraic structures where the module operations and group actions are subject to approximation, based on lower and upper bounds. Also, we define and investigate rough injective G-modules, which generalize the classical concept of injectivity under rough approximations. We examine their structural properties, provide characterizations, and explore their behavior under homomorphisms and extensions. The paper establishes key embedding theorems and extension criteria, ensuring the compatibility of injectivity with rough approximation operators. The practical relevance of these theoretical developments through an application to data access control systems is provided where user permissions and role hierarchies naturally exhibit rough and uncertain relationships. Our results offer a novel algebraic framework for reasoning about access privileges in the presence of partial or uncertain information, thus highlighting the potential of rough G-module theory in real-world computational settings.
KEYWORDS
Rough Set Theory, Upper Approximation, Lower Approximation, G Modules, Rough G Modules, Rough Injective G Modules
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] S. Sangeetha , Shakeela Sathish , B. Muthu Deepika , B. Srirekha , "Rough Injective G-Modules," Mathematics and Statistics, Vol. 13, No. 5, pp. 337 - 344, 2025. DOI: 10.13189/ms.2025.130509.
(b). APA Format:
S. Sangeetha , Shakeela Sathish , B. Muthu Deepika , B. Srirekha (2025). Rough Injective G-Modules. Mathematics and Statistics, 13(5), 337 - 344. DOI: 10.13189/ms.2025.130509.