Taiwanese Journal of Mathematics

Jordan $\tau$-derivations of Prime GPI-rings

Jheng-Huei Lin

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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 $\operatorname{deg} \tau^{2} \neq 2$.

Article information

Taiwanese J. Math., Advance publication (2019), 15 pages.

First available in Project Euclid: 18 November 2019

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Primary: 16R60: Functional identities 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16W10: Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 16W25: Derivations, actions of Lie algebras

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


Lin, Jheng-Huei. Jordan $\tau$-derivations of Prime GPI-rings. Taiwanese J. Math., advance publication, 18 November 2019. doi:10.11650/tjm/191105. https://projecteuclid.org/euclid.twjm/1574046020

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