Open Access
Translator Disclaimer
October, 2020 Jordan $\tau$-derivations of Prime GPI-rings
Jheng-Huei Lin
Taiwanese J. Math. 24(5): 1091-1105 (October, 2020). DOI: 10.11650/tjm/191105


Let $R$ be a noncommutative prime ring, with maximal symmetric ring of quotients $Q_{ms}(R)$ and extended centriod $C$, and let $\tau$ be an anti-automorphism of $R$. An additive map $\delta \colon R \to Q_{ms}(R)$ is called a Jordan $\tau$-derivation if $\delta(x^2) = \delta(x) x^{\tau} + x\delta(x)$ for all $x \in R$. In 2015 Lee and the author proved that any Jordan $\tau$-derivation of $R$ is X-inner if either $R$ is not a GPI-ring or $R$ is a PI-ring except when $\operatorname{char}R = 2$ and $\dim_C RC = 4$. In the paper we prove that, when $R$ is a prime GPI-ring but is not a PI-ring, any Jordan $\tau$-derivation is X-inner if either $\tau$ is of the second kind or both $\operatorname{char}R \neq 2$ and $\tau$ is of the first kind with $\operatorname{deg} \tau^{2} \neq 2$.


Download Citation

Jheng-Huei Lin. "Jordan $\tau$-derivations of Prime GPI-rings." Taiwanese J. Math. 24 (5) 1091 - 1105, October, 2020.


Received: 14 October 2019; Revised: 8 November 2019; Accepted: 14 November 2019; Published: October, 2020
First available in Project Euclid: 18 November 2019

MathSciNet: MR4152657
Digital Object Identifier: 10.11650/tjm/191105

Primary: 16N60 , 16R60 , 16W10 , 16W25

Keywords: (X-inner) Jordan $\tau$-derivation , anti-automorphism , functional identity , maximal symmetric ring of quotients , PI-ring , prime GPI-ring

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 5 • October, 2020
Back to Top