On derivations and commutativity of prime rings with involution

被引:23
|
作者
Ali, Shakir [1 ]
Dar, Nadeem Ahmed [1 ]
Asci, Mustafa [2 ]
机构
[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India
[2] Pamukkale Univ, Dept Math, TR-20100 Denizli, Turkey
关键词
Prime ring; normal ring; involution; derivation; SEMIPRIME; MAPPINGS;
D O I
10.1515/gmj-2015-0016
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In [6], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d (xy) = d (yx) for all x, y is an element of R, then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d (xx*) = d (x*x) for all x is an element of R and S(R) boolean AND Z(R) not equal (0), then R is commutative. Moreover, some related results have also been discussed.
引用
收藏
页码:9 / 14
页数:6
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