A Study of Triple Derivations, Jordan UGeneralized of Semiprime Rings

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Abstract

Within the scope of this work, we prove, among other things, that if d is a Jordan derivation of asemiprime ring R, then R is a Jordan derivation of d, then d is a quarter derivation. Because of this, we areable to show that d can be derived three times. We further prove that if and only if R is a semiprime ring ofcharacter 2, and d acts as a homomorphism on R, then d is a central derivation. We prove that eachsemiprime ring R of character 2 with a u-generalized derivation G also has a corresponding u-generalizedderivation G. Similarly, we prove that G is a u-generalized derivation if and only if R is an asemiprimering of character 2. We also establish that R is commutative if and only if .