Study of Generalized Derivations in Rings with Involution

被引:1
作者
Mozumder, Muzibur Rahman [1 ]
Abbasi, Adnan [1 ]
Dar, Nadeem Ahmad [2 ]
机构
[1] Aligarh Muslim Univ, Dept Math, Aligarh, Uttar Pradesh, India
[2] Govt HSS, Shopian, Jammu & Kashmir, India
来源
KYUNGPOOK MATHEMATICAL JOURNAL | 2019年 / 59卷 / 01期
关键词
prime ring; generalized derivation; derivation; involution; COMMUTATIVITY; PRIME;
D O I
10.5666/KMJ.2019.59.1.1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let R be a prime ring with involution of the second kind and centre Z(R). Suppose R admits a generalized derivation F : R -> R associated with a derivation d : R -> R. The purpose of this paper is to study the commutativity of a prime ring R satisfying any one of the following identities: (i) F(x) circle x* is an element of Z(R) (ii) F([x, x*]) +/- x circle x* is an element of Z(R) (iii) F(x circle x*) +/- [x, x*] is an element of Z(R) (iv) F(x) circle d(x*) +/- x circle x* is an element of Z(R) (v) [F(x), d(x*)] +/- x circle x* is an element of Z(R) (vi) F(x) +/- x circle x* is an element of Z(R) (viii) F(x) +/- [x, x*] is an element of Z(R) (viii) [F(x), x*] -/+ F(x) circle x* is an element of Z(R) (ix) F(x circle x*) is an element of Z(R) for all x is an element of R.
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页码:1 / 11
页数:11
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