Identities related to generalized derivation on ideal in prime rings

被引：23

作者：

Tiwari S.K. ^{[1
]}

Sharma R.K. ^{[1
]}

Dhara B. ^{[2
]}

机构：

[1] Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi

[2] Department of Mathematics, Belda College, Belda, Paschim Medinipur

来源：

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry | 2016年 / 57卷 / 4期

关键词：

Derivation; Generalized derivation; Prime ring;

D O I：

10.1007/s13366-015-0262-6

中图分类号：

学科分类号：

摘要：

Let R be a prime ring with center Z(R), I a non-zero ideal of R and α: R→ R any mapping on R. Suppose that G and F are two generalized derivations associated with derivations g and d respectively on R. In this paper we study the following situations: (i) G(xy) ± F(x) F(y) ± xy∈ Z(R) , (ii) G(xy) ± F(y) F(x) ± xy∈ Z(R) , (iii) G(xy) ± F(x) F(y) ± yx∈ Z(R) , (iv) G(xy) ± F(y) F(x) ± yx∈ Z(R) , (v) G(xy) ± F(y) F(x) ± [ x, y] ∈ Z(R) , (vi) G(xy) ± F(x) F(y) ± [ α(x) , y] ∈ Z(R) for all x, y∈ I. Further an example is given to show that the primeness condition is not superfluous. © 2015, The Managing Editors.

引用

页码：809 / 821

页数：12

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