On intuitionistic fuzzy prime and G-prime ideals of a near ring
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Group actions are a valuable tool for investigating the symmetry and automorphism features of near-rings. In this paper, we introduce group action on intuitionistic fuzzy (IF) ideals of near ring $\mathcal{N}$. We define intrinsic product of IF ideals of $\mathcal{N}$ and investigate some properties of IF prime ideals under group action on it. Moreover, we develop an idea of IF $\mathcal{G}$-prime ideal of $\mathcal{N}.$ Moreover, we show that for an IF ideal $\mathcal{F}$ of $\mathcal{N}$ such that $\mathcal{F}^{\mathcal{G}}= \underset{g \in \mathcal{G}}{\cap} \mathcal{F}^{g},$ then $\mathcal{F}^{\mathcal{G}}$ is the largest $\mathcal{G}$-invariant IF ideal of $\mathcal{N}$ contained in $\mathcal{F}$. We additionally prove that $\mathcal{G}$-primeness of $\mathcal{F}^{\mathcal{G}}$ is uniquely determined by $\mathcal{G}$-primeness of $\mathcal{F}$ upto $\mathcal{G}$-orbits.
Abstract
Group actions are a valuable tool for investigating the symmetry and automorphism features of near-rings. In this paper, we introduce group action on intuitionistic fuzzy (IF) ideals of near ring $\mathcal{N}$. We define intrinsic product of IF ideals of $\mathcal{N}$ and investigate some properties of IF prime ideals under group action on it. Moreover, we develop an idea of IF $\mathcal{G}$-prime ideal of $\mathcal{N}.$ Moreover, we show that for an IF ideal $\mathcal{F}$ of $\mathcal{N}$ such that $\mathcal{F}^{\mathcal{G}}= \underset{g \in \mathcal{G}}{\cap} \mathcal{F}^{g},$ then $\mathcal{F}^{\mathcal{G}}$ is the largest $\mathcal{G}$-invariant IF ideal of $\mathcal{N}$ contained in $\mathcal{F}$. We additionally prove that $\mathcal{G}$-primeness of $\mathcal{F}^{\mathcal{G}}$ is uniquely determined by $\mathcal{G}$-primeness of $\mathcal{F}$ upto $\mathcal{G}$-orbits.