Browsing by Author "NITIN BHARDWAJ"

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    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.