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Submitted
February 12, 2022
Accepted
February 1, 2023
Published
March 30, 2023
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Abstract

In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N −subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals.

Keywords

Sheffer stroke BCK-algebra subalgebra ideal neutrosophic N − subalgebra neutrosophic N −ideal

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How to Cite
Oner, T., Katican, T., & Rezaei, A. (2023). Neutrosophic N−Ideals on Sheffer Stroke BCK-Algebras. Journal of the Indonesian Mathematical Society, 29(1), 45–63. https://doi.org/10.22342/jims.29.1.1165.45-63
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