关于具有广义导数的素环的一个结果

Q4 Mathematics Discussiones Mathematicae - General Algebra and Applications Pub Date : 2021-09-06 DOI:10.7151/dmgaa.1373

F. Shujat, Shahoor Khan

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引用次数: 0

摘要

本文对以下结果进行了研究。设R为素环，Q为对称Martindale商环，C为扩展质心，I为R的非零理想。若F和G是R的两个广义导数，使得(F(xy) + G(yx))n−(xy / yx)n = 0，对于所有x∈y∈I，则R是可交换的，或者F(x) = x, G(x) =可/ / x对于所有x∈R, n = 1。

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A Result on Prime Rings with Generalized Derivations

Abstract In this paper we investigate the following result. Let R be a prime ring, Q its symmetric Martindale quotient ring, C its extended centroid, I a nonzero ideal of R. If F and G are the two generalized derivation of R such that (F(xy) + G(yx))n − (xy ∓ yx)n = 0, for all x, y ∈ I, then either R is commutative or F (x) = x, G(x) = ∓x for all x ∈ R and n = 1.

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