Fuzzy Nilpotent Ideals in BCK-Algebras

E. Mohammadzadeh, G. Muhiuddin and R. A. Borzooei
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E. Mohammadzadeh: Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran
G. Muhiuddin: ��Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
R. A. Borzooei: ��Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran

New Mathematics and Natural Computation (NMNC), 2024, vol. 20, issue 01, 233-245

Abstract: One of the most critical concepts in the study of groups is the notion of nilpotency. Nilpotent groups arise in Galois theory, as well as in the classification of groups. In this paper, we apply the notion of nilpotency on BCK-algebras by using fuzzy ideals. First we define the concept of nilpotent fuzzy ideal in BCK-algebras and investigate their properties. Furthermore, we find some relation between fuzzy nilpotent ideals and quotient BCK-algebras. Specially, we construct a nilpotent BCK-algebra by using a fuzzy nilpotent ideal. Finally, we prove that any minimal ideals of a BCK-algebra X, is contained in the center of any fuzzy nilpotent ideals of X.

Keywords: (Commutative) BCK-algebras; nilpotent BCK-algebra; fuzzy nilpotent ideal (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S1793005724500133

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