Fuzzy Neutrosophic Prime Ideals of BCK-algebras.

Document Type : Other

Authors

1 SIR C R REDDY COLLEGE OF ENGINEERING,ELURU-534 007

2 Department of Mathematics, Acharaya Nagarjuna University, Nagarjuna Nagar, Guntur-522 510

3 Department of Mathematics, Government Degree college, Chitalapudi-534 460.

10.22044/jas.2023.12903.1701

Abstract

In this research paper, we introduce and analyze the notion of fuzzy neutrosophic prime ideals (FNPIs) in a commutative BCK-algebra $\mathcal{K}$. It represents a further extension of prime ideals in the context of fuzzy neutrosophic sets. We provide an example that shows that not every fuzzy neutrosophic ideal of a commutative BCK-algebra $\mathcal{K}$ is a FNPI of $\mathcal{K}$. We also prove that a fuzzy neutrosophic set of $\mathcal{K}$ is a FNPI of $\mathcal{K}$ if, for all $a,b,c \in [0,1] $, the upper (a,b)-level cut and lower c-level cut are prime ideals of $\mathcal{K}$.

Keywords

Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 09 April 2024

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