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 [Formula: see text]([Formula: see text]). Moreover, we proved that for a fuzzy hyperring S, the quotient [Formula: see text]([Formula: see text]) 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
• 17B62
• 20N20