Jordan f-Derivations on Prime and Semiprime Rings

Annual Meeting in Mathematics 2023

Abstract

Let $R$ be a ring and $f : R\rightarrow R$ be a mapping. A mapping $D : R\rightarrow R$ is said to be a $Jordan\ f-derivation$ on $R$ if $D(a+b) = D(a) + D(b)$ for all $a, b\in R$, and $D(a^2) = D(a)f(a) + f(a)D(a)$ for all $a \in R.$ In this paper, we present some conditions on prime ring or semiprime ring $R$ that force the zero map to be the only Jordan $f$-derivation on $R$.