On ideals and commutativity of prime rings with generalized derivations

被引:9
作者
Abu Nawas, M. K. [1 ]
Al-Omary, Radwan M. [2 ]
机构
[1] Northern Border Univ, Fac Sci, Dept Math, Ar Ar, Saudi Arabia
[2] Ibb Univ, Dept Math, Ibb, Yemen
来源
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2018年 / 11卷 / 01期
关键词
Left ideals; prime rings; centralizing; derivations; generalized derivations; commutativity;
D O I
10.29020/nybg.ejpam.v11i1.3142
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
An additive mapping F: R -> R is called a generalized derivation on R if there exists a derivation d: R R such that F(xy) = xF(y) d(x)y holds for all x, y is an element of R. It is called a generalized (alpha, beta) derivation on R if there exists an (alpha,beta) derivation d: R -> R such that the equation F(xy) = F(x)alpha(y),beta(x)d(y) holds for all x, y is an element of R. In the present paper, we investigate commutativity of a prime ring R, which satisfies certain differential identities on the left ideals of R. Moreover some results on commutativity of rings with involutions that satisfy certain identities are proved.
引用
收藏
页码:79 / 89
页数:11
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