THE SUFFICIENT CONDITIONS FOR A MULTIPLICATIVE DERIVATION IN THE JORDAN RING TO BE ADDITIVE

Derivation is a mapping from a set to itself. There are two types of derivations in rings: ordinary derivation and Jordan derivation. Given a triangular matrix ring T, a non-associative ring can be formed, known as a Jordan ring T. Subsequently, on the Jordan ring T, a derivation can be defined, referred to as derivation in the Jordan ring T. This paper provides the conditions that must be met for a multiplication derivation on the Jordan ring T to be additive. Furthermore, the ring T must be 2-torsion-free so that the derivation on the Jordan ring becomes a Jordan derivation on the ring T.