Further results on(âˆˆ,âˆˆ)-neutrosophic subalgebras and ideals inBCK/BCI-algebras

G.  Muhiuddin; Hashem  Bordbar; Florentin Smarandache; Young Bae  Jun

Further results on(âˆˆ,âˆˆ)-neutrosophic subalgebras and ideals inBCK/BCI-algebras

Authors

G. Muhiuddin Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
Hashem Bordbar Postdoctoral Research Fellow, Shahid Beheshti University, Tehran, Iran
Florentin Smarandache University of New Mexico, Math & Science Division, 705 Gurley Ave., Gallup, NM 87301, USA
Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea.

Keywords:

(âˆˆ,âˆˆ)-neutrosophic subalgebra,(âˆˆ,âˆˆ)-neutrosophic ideal

Abstract

Characterizations of an(âˆˆ,âˆˆ)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some(âˆˆ,âˆˆ)-neutrosophic ideal. The relation between(âˆˆ,âˆˆ)-neutrosophic ideal and(âˆˆ,âˆˆ)-neutrosophic subalgebra in aBCK-algebra is discussed. Conditions for an(âˆˆ,âˆˆ)-neutrosophic subalgebra to be a(âˆˆ,âˆˆ)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an(âˆˆ,âˆˆ)-neutrosophic ideal is established. Equivalence relations on the family of all(âˆˆ,âˆˆ)-neutrosophic ideals are introduced, and related properties are investigated

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Published

2018-04-28

Issue

Vol. 20 (2018): Neutrosophic Sets and Systems

Section

SI#1,2024: Neutrosophical Advancements And Their Impact on Research

License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Creative Commons Attribution (CC BY) license.

How to Cite

Muhiuddin, G. ., Bordbar, H. ., Smarandache, F., & Jun, Y. B. (2018). Further results on(âˆˆ,âˆˆ)-neutrosophic subalgebras and ideals inBCK/BCI-algebras. Neutrosophic Sets and Systems, 20, 36-43. https://fs.unm.edu/nss8/index.php/111/article/view/282