Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

Abstract

In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation ${\zeta }_n^{\ast }$(${\nu }_{n,s}^{\ast }$). Moreover, we proved that for a fuzzy hyperring S, the quotient $S/{\zeta }_n^{\ast }$($S/{\nu }_{n,s}^{\ast }$) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.

Keywords:

• (Nilpotent) Lie ring
• Engel Lie ring
• fuzzy hyperring
• strongly regular relation

MSC (2010):

• 17B62
• 20N20

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

E. Mohammadzadeh

E. Mohammadzadeh is assistant professor at the Payame Noor University, Iran. She has published more than 20 papers in the international journals. Her main scientific interests are algebraic logic, algebraic hyperstructures and fuzzy algebras.

R. A. Borzooei

R. A. Borzooei is full professor at the Shahid Beheshti University, Tehran, Iran. He is currently, Editor In-Chief and founder of “Iranian Journal of Fuzzy Systems” and “Journal of Algebraic Hyperstructures and Logical”, editorial board of six international journals. He has published more than 330 papers in the international journals. His main scientific interests are algebraic logics, ordered algebraic structures, algebraic hyperstructures, fuzzy algebras and fuzzy graphs.

F. Mohammadzadeh

F. Mohammadzadeh is assistant professor at the Payame Noor University, Tehran, Iran. Her main scientific interests are algebraic hyperstructures and fuzzy algebras.

S. S. Ahn

S. S. Ahn is full professor at the Dongguk University, Korea. She works in the Department of Mathematics Education from 1993 to present. She has published more than 150 papers in the international journals. Her main scientific interests are logical algebras, ordered algebras, algebraic hyperstructures, fuzzy algebras and fuzzy graphs.