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Neutrosophic $\mathcal{N}-$structures on Sheffer stroke BE-algebras | ||
| Journal of Mahani Mathematical Research | ||
| دوره 11، شماره 1 - شماره پیاپی 21، فروردین 2022، صفحه 121-143 اصل مقاله (522.8 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.18565.1176 | ||
| نویسندگان | ||
| Tahsin Oner* 1؛ Tugce Katican2؛ Salviya Svanidze1؛ Akbar Rezaei3 | ||
| 1Department of Mathematics, Ege University, Izmir, Turkey | ||
| 2Department of Mathematics, Izmir University of Economics, Izmir, Turkey | ||
| 3Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| In this study, a neutrosophic $\mathcal{N}-$subalgebra, a (implicative) neutrosophic $\mathcal{N}-$ filter, level sets of these neutrosophic $\mathcal{N}-$structures and their properties are introduced on a Sheffer stroke BE-algebras (briefly, SBE-algebras). It is proved that the level set of neutrosophic $\mathcal{N}-$ subalgebras ((implicative) neutrosophic $\mathcal{N}-$filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then we present relationships between upper sets and neutrosophic $\mathcal{N}-$filters of this algebra. Also, it is given that every neutrosophic $\mathcal{N}-$filter of a SBE-algebra is its neutrosophic $\mathcal{N}-$subalgebra but the inverse is generally not true. We study on neutrosophic $\mathcal{N}-$filters of SBE-algebras by means of SBE-homomorphisms, and present relationships between mentioned structures on a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of $\mathcal{N}-$functions and some properties are examined. | ||
| کلیدواژهها | ||
| SBE-algebra؛ (implicative) SBE-filter؛ neutrosophic N− subalgebra؛ (implicative) neutrosophic N−filter | ||
| مراجع | ||
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