On the intuitionistic fuzzy polynomial ideals of a ring

Transstellar Journal , 2019

In this paper, we introduce the concept of-intuitionistic fuzzy ideal and-intuitionistic fuzzy ideal and study their properties.

IJMS, 2012

In this paper, we apply the Yuanli, Zhang, Quanma's idea of intuitionistic anti-fuzzy subgroups to subring and ideal of a ring. We introduce the notion of intuitionistic anti-fuzzy subring and intuitionistic anti-fuzzy ideal of rings, and investigate some related properties.

Palestine Journal of Mathematics, 2024

In this paper, we introduce the notion of expansion of intuitionistic fuzzy ideals of a commutative Γ-ring and by using this concept, we develop the notion of intuitionistic fuzzy f-primary ideals (2-absorbing f-primary ideals) which unify the notion of intuitionistic fuzzy prime ideals (2-absorbing ideals) and intuitionistic fuzzy primary ideals (2-absorbing primary ideals) of Γ-ring. A number of important results about intuitionistic fuzzy prime ideals (2-absorbing ideals) and intuitionistic fuzzy primary ideals (2-absorbing primary ideals) are extended into this general frame work.

Notes on Intuitionistic Fuzzy Sets

In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an Aγ-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.

Creative Mathematics and Informatics, 2022

In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in Γ-rings. We also characterise intuitionistic fuzzy primary ideal of Γ-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of Γ-rings.

Notes on IFS, 2022

In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an A γ-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.

Palestine Journal of Mathematics, 2025

Keywords and phrases: Γ-ring, Extensions of intuitionistic fuzzy ideal, Intuitionistic fuzzy prime (semiprime) ideal. The authors would like to thank the reviewers and editor for their constructive comments and valuable suggestions that improved the quality of our paper. Hem Lata extends her appreciation to LPU, Phagwara for imparting the chance to carry forward her research work..

International Journal of Mathematics and Computer Science, 2018

In this paper, we further study the theory of intuitionistic fuzzy rings and give some new concepts such as intuitionistic fuzzy ring with operators, intuitionistic fuzzy ideal with operators , intuitionistic fuzzy quotient ring with operators, etc. while their some elementary properties are discussed.

CREAT.MATH.INFORM., 2024

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.

International Journal of Algebra, 2011

In this paper we present a new formulation of intuitionistic fuzzy rings based on the notion of intuitionistic fuzzy space. A relation between intuitionistic fuzzy ring based on intuitionistic fuzzy space and ordinary rings is obtained in terms of induction and ...