Research Articles

Permanent URI for this collection

http://davjalandhar.ndl.gov.in/handle/123456789/178

Browse

Browsing Research Articles by Author "P. K. SHARMA"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    A STUDY ON GROUP ACTION ON INTUITIONISTIC FUZZY PRIMARY AND SEMIPRIMARY IDEALS
    (TWMS Journal of Applied and Engineering Mathematics, Vol.15, No.3, 2025) P. K. SHARMA
    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 P G = 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.
  • No Thumbnail Available
    Item
    Decomposition Of Intuitionistic Fuzzy Primary Ideals Of Γ-Rings
    (CREAT. MATH. INFORM., 2024) P. K. SHARMA; HEM LATA; NITIN BHARDWAJ
    ABSTRACT. In this paper, we establish the intuitionistic fuzzy version of the Lasker-Noether theorem for a commutative Γ-ring. We show that in a commutative Noetherian Γ-ring, every intuitionistic fuzzy ideal A can be decomposed as the intersection of a finite number of intuitionistic fuzzy irreducible ideals (primary ideals). This decomposition is called an intuitionistic fuzzy primary decomposition. Further, we show that in case of a minimal intuitionistic fuzzy primary decomposition of A, the set of all intuitionistic fuzzy associated prime ideals of A is independent of the particular decomposition. We also discuss some other fundamental results pertaining to this concept.