Decomposition Of Intuitionistic Fuzzy Primary Ideals Of Γ-Rings
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Date
2024
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CREAT. MATH. INFORM.
Abstract
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.