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(& lowast;)(n)(nu(& lowast;)(n,s)). Moreover, we proved that for a fuzzy hyperring S, the quotient S/zeta(& lowast;)(n)(S/nu(& lowast;)(n,s)) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of . Also, we studied the relation-ship between the strongly regular relation and-role of a given fuzzy hyperring.