On NJ-Ternary Rings in Graded Ternary Rings

Abstract

This paper introduces the concept of an NJ-ternary ring and investigates its properties within the framework of graded ternary rings. Particular attention is given to the relationship between a graded NJ-ternary ring and its homogeneous components. It is shown that the identity component of a graded NJ-ternary ring is itself an NJ-ternary ring, whereas every non-identity homogeneous component consists entirely of quasi-regular elements. These results provide further insight into the structural behavior of NJ-ternary rings under grading. The study also examines the relationship between JR-ternary rings and NJ-ternary rings in the graded setting, highlighting connections between these classes of ternary rings and their associated radical properties. The findings contribute to the development of the theory of graded ternary rings and provide a foundation for further investigation of NJ-type structures and Jacobson radical behavior in ternary algebraic systems.