Intuitionistic Fuzzy Polynomial Ideals Of A Poynomial Ring And Its Nil Radical Structure (original) (raw)

On the intuitionistic fuzzy polynomial ideals of a ring

In this paper we introduce the notion of intuitionistic fuzzy polynomial ideal A x of a polynomial ring R[x] induced by an intuitionistic fuzzy ideal A of a ring R, and obtain an isomorphism theorem of a ring of intuitionistic fuzzy cosets of A x. It is shown that an intuitionistic fuzzy ideal A of a ring is an intuitionistic fuzzy prime if and only if A x is an intuitionistic fuzzy prime ideal of R[x]. Moreover, we show that if A x is an intuitionistic fuzzy maximal ideal of R[x], then A is an intuitionistic fuzzy maximal ideal of R but converse is not true.

Radical structures of intuitionistic fuzzy polynomial ideals of a ring

Notes on Intuitionistic Fuzzy Sets, 2018

In this paper we investigate the radical structure of an intuitionistic fuzzy polynomial ideal A x induced by an intuitionistic fuzzy ideal A of a ring and study its properties. Given an intuitionistic fuzzy ideal B of a ring R and a homomorphism f : R → R , we show that if f x : R[x] → R [x] is the induced homomorphism of f , that is, f x (n i=0 a i x i) = n i=0 (f (a i))x i , then f −1 x [(√ B) x ] = (f −1 (B)) x .

Intuitionistic Fuzzy Prime Radical and Intuitionistic Fuzzy Primary Ideal Of Γ-Ring

Creative Mathematics and Informatics, 2023

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.

ON INTUITIONISTIC FUZZY PRIMARY IDEAL OF A RING

Pan-American Journal of Mathematics, 2022

The purpose of this paper is to introduce and investigate primary ideal and P-primary ideal in the intuitionistic fuzzy environment and lay down the foundation for the primary decomposition theorem in the intuitionistic fuzzy setting. Also a suitable characterization of intuitionistic fuzzy P-primary ideal will be discussed.

INTUITIONISTIC FUZZY IDEALS

Transstellar Journal , 2019

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

Intuitionistic Fuzzy Normed Prime Ideal and Some of Their Characteristics

2021

This Paper intends to introduce the notion of prime ideals of Intuitionistic fuzzy normed Rings and to establish basic properties related to it. It investigates these notions and shown anew Result using intuinistic fuzzy points and non membership function incorparating with t-norm and s-norm to show aome results of fuzzy prime ideal.

ON INTUITIONISTIC ANTI-FUZZY IDEAL IN RINGS

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.

On Intuitionistic Fuzzy f -Primary Ideals Of Commutative Γ-Rings

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.