素环中广义衍生的乔丹同源行为

Pub Date : 2024-02-20 DOI:10.1007/s11253-024-02265-3

Nripendu Bera, Basudeb Dhara

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引用次数: 0

摘要

假设 R 是质环，char(R) ≠ 2，f(ξ1, ... , ξn) 是 C(= Z(U))上的非中心多线性多项式，其中 U 是 R 的乌图米商环。如果对于所有 a, b∈ R，h(ab) = h(a)h(b)+h(a)b+ah(b) ，则加法映射 h : R ⟶ R 称为同化。对于所有ξ∈ f(R) = {f(ξ1，., ξn) | ξ1, ., ξn∈ R}。

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Jordan Homoderivation Behavior of Generalized Derivations in Prime Rings

Suppose that R is a prime ring with char(R) ≠ 2 and f(ξ₁, . . . , ξ_n) is a noncentral multilinear polynomial over C(= Z(U)), where U is the Utumi quotient ring of R. An additive mapping h : R ⟶ R is called homoderivation if h(ab) = h(a)h(b)+h(a)b+ah(b) for all a, b ∈ R. We investigate the behavior of three generalized derivations F, G, and H of R satisfying the condition

\(F\left({\xi }^{2}\right)=G\left({\xi }^{2}\right)+H\left(\xi \right)\xi +\xi H\left(\xi \right)\)

for all ξ ∈ f(R) = {f(ξ₁, . . . , ξ_n) | ξ₁, . . . , ξ_n ∈ R}.

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