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

Dyana Patty

doi:10.30598/parameterv4i1pp95-110

Dyana Patty Mathematic Department, Faculty of Mathematics and Natural Sciences, Universitas Pattimura, Indonesia

DOI: https://doi.org/10.30598/parameterv4i1pp95-110

Keywords: Derivation, Jordan Derivation, Triangular Matrix Ring

Abstract

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 , a non-associative ring can be formed, known as a Jordan ring T. Subsequently, on the Jordan ring , a derivation can be defined, referred to as derivation in the Jordan ring . This paper provides the conditions that must be met for a multiplication derivation on the Jordan ring to be additive. Furthermore, the ring must be -torsion-free so that the derivation on the Jordan ring becomes a Jordan derivation on the ring .

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