A Study of Triple Derivations, Jordan UGeneralized of Semiprime Rings
by Rani Tiwari*, Dr. Birendra Kumar Chauhan,
- Published in Journal of Advances and Scholarly Researches in Allied Education, E-ISSN: 2230-7540
Volume 18, Issue No. 4, Jul 2021, Pages 1118 - 1121 (4)
Published by: Ignited Minds Journals
ABSTRACT
Within the scope of this work, we prove, among other things, that if d is a Jordan derivation of a semiprime ring R, then R is a Jordan derivation of d, then d is a quarter derivation. Because of this, we are able to show that d can be derived three times. We further prove that if and only if R is a semiprime ring of character 2, and d acts as a homomorphism on R, then d is a central derivation. We prove that each semiprime ring R of character 2 with a u-generalized derivation G also has a corresponding u-generalized derivation G. Similarly, we prove that G is a u-generalized derivation if and only if R is an asemiprime ring of character 2. We also establish that R is commutative if and only if .
KEYWORD
triple derivations, Jordan UGeneralized, semiprime rings, Jordan derivation, quarter derivation, homomorphism, central derivation, u-generalized derivation, asemiprime ring, commutative
