On Semiprime Rings with ({\alpha},{\alpha})-Symmetric Derivations

TL;DR

This paper investigates ({eta},{eta})-symmetric derivations on semiprime and prime rings, providing new results on their properties under certain conditions, expanding understanding of ring automorphisms and derivations.

Contribution

It introduces new results on ({eta},{eta})-symmetric derivations in semiprime rings, highlighting their behavior under specific conditions.

Findings

Characterization of ({eta},{eta})-symmetric derivations on semiprime rings

Conditions under which derivations satisfy symmetry properties

Insights into automorphism interactions with derivations

Abstract

The main purpose of this paper is to study and investigate concerning a ({\alpha},{\alpha})-symmetric derivations D on semiprime rings and prime rings R, we give some results when R admits a ({\alpha},{\alpha})-symmetric derivations D to satisfy some conditions on R.Where {\alpha}: R to R is an automorphism mapping.