Issue:An investigation of group action on intuitionistic fuzzy primary and semiprimary ideals of Γ-ring

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Title of paper: An investigation of group action on intuitionistic fuzzy primary and semiprimary ideals of Γ-ring Author(s): Poonam Kumar Sharma     0000-0001-5463-8665 Post-Graduate Department of Mathematics, D. A. V. College, Jalandhar, Punjab, India pksharma@davjalandhar.com Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 358–371 DOI: https://doi.org/10.7546/nifs.2025.31.3.358-371 Download:  PDF (277  Kb, File info) Abstract: This article is a continuation of the author’s earlier work [11]. Here we extend the study of group actions on intuitionistic fuzzy structures by focusing on intuitionistic fuzzy primary and semiprimary ideals of Γ-rings. We introduce and characterize intuitionistic fuzzy G-primary and G-semiprimary ideals, establishing their relationships with G-invariant intuitionistic fuzzy ideals. Several structural properties and related results are investigated to deepen the understanding of these generalized ideals under group actions. Furthermore, we explore the behavior of intuitionistic fuzzy G-primary and G-semiprimary ideals under G-homomorphisms, specifically analyzing their image and pre-image. These results contribute to the ongoing development of intuitionistic fuzzy algebraic structures in the context of Γ-rings. Keywords: Intuitionistic fuzzy primary (semiprimary) ideals, Intuitionistic fuzzy G-primary (G-semiprimary) ideals, Radical of an intuitionistic fuzzy G-ideal, G-homomorphism. AMS Classification: 03E72, 03F55, 13A50, 16N40, 16N60, 16W25. References: Atanassov, K. T. (1983). Intuitionistic fuzzy sets. In: Sgurev, V. (Ed.). VII ITKR’s Session. Deposited in: Central Science and Technology Library of the Bulgarian Academy of Sci, Sofia. Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6. Atanassov, K. T. (1986). Intuitionistic fuzzy Sets. Fuzzy Sets and Systems, 20(1), 87–96. Barnes, W. E. (1966). On the Γ-rings of Nobusawa. Pacific Journal of Mathematics, 18, 411–422. Kim, K. H., Jun, Y. B., & Ozturk, M. A. (2001). Intuitionistic fuzzy Γ-ideals of Γ-rings. Scienctiae Mathematicae Japonicae Online, 4, 431–440. Kyuno, S. (1982). Prime ideals in gamma rings. Pacific Journal of Mathematics, 98(2), 375–379. Nobusawa, N. (1964). On a generalization of the ring theory. Osaka Journal of Mathematics, 1(1), 81–89. Palaniappan, N., & Ramachandran, M. (2011). Intuitionistic fuzzy prime ideals in Γ-rings. International Journal of Fuzzy Mathematics and Systems, 1(2), 141–153. Palaniappan, N., Veerappan, P. S., & Ramachandran, M. (2010). Characterization of intuitionistic fuzzy ideals of Γ-rings. Applied Mathematical Sciences, 4(23), 1107–1117. Palaniappan, N., Veerappan, P. S., & Ramachandran, M. (2011). Some properties of intuitionistic fuzzy ideals of Γ-rings. Thai Journal of Mathematics, 9(2), 305–318. Paul, R. (2015). On various types of ideals of Γ-rings and the corresponding operator rings. International Journal of Engineering Research and Applications, 5(8) 95–98. Sharma, P. K. (2025). Group action on intuitionistic fuzzy ideals of Γ-ring. Notes on Intuitionistic Fuzzy Sets, 31(2), 139–153. Sharma, P. K., & Lata, H. (2022). Intuitionistic fuzzy characteristic ideals of a Γ-ring. South East Asian Journal of Mathematics and Mathematical Sciences, 18(1), 49–70. Sharma, P. K., Lata, H., & Bhardwaj, N. (2022). On intuitionistic fuzzy structure space on Γ-ring. Creative Mathematics and Informatics, 31(2), 215–228. Sharma, P. K., Lata, H., & Bhardwaj, N. (2023). Intuitionistic fuzzy prime radical and intuitionistic fuzzy primary ideal of Γ-ring. Creative Mathematics and Informatics, 32(1), 69–86. Sharma, P. K., Lata, H., & Bhardwaj, N. (2024). Decomposition of intuitionistic fuzzy primary ideal of Γ-ring. Creative Mathematics and Informatics, 33(1), 65–75. Sharma, P. K., Lata, H., & Bhardwaj, N. (2025). Extension of intuitionistic fuzzy ideal of Γ-rings. Palestine Journal of Mathematics, 14(1), 444–455. Warsi, Z. K. (1978). On decomposition of primary ideals of Γ-rings. Indian Journal of Pure and Applied Mathematics, 9(9), 912–917. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353 Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.