A study on group action on intuitionistic fuzzy primary and semiprimary ideals

Abstract

Group actions are a useful technique for examining the symmetry and automorphism characteristics of rings. The concept of intuitionistic fuzzy ideals in rings has been broadened with the inclusion of the concepts of intuitionistic fuzzy primary and semiprimary ideals. The purpose of this article is to extend the group action to the intuitionistic fuzzy ideals of a ring R with group action on it and to derive a relation between the intuitionistic fuzzy G-primary (G-semiprimary) ideals and the intuitionistic fuzzy primary (semiprimary) ideals of R. We established that the largest G-invariant intuitionistic fuzzy ideal contained in an intuitionistic fuzzy primary (semiprimary) ideal is an intuitionistic fuzzy G-primary (G-semiprimary) ideal of R. Conversely, if Q is an intuitionistic fuzzy G-primary (G-semiprimary) ideal of R, then there exists an intuitionistic fuzzy primary (semiprimary) ideal P of R such that Pᴳ = Q. We also investigate the relationships between the intuitionistic fuzzy G-primary (G-semiprimary) ideals of R and their level cuts under this group action. Additionally, we establish a suitable characterization of intuitionistic fuzzy G-primary (G-semiprimary) ideals of R in terms of intuitionistic fuzzy points in R under this group action. In addition to these, we also investigate the preservation of the image and pre-image of an intuitionistic fuzzy G-primary (G-semiprimary) ideal of a ring under G-homomorphism.