SOME COMMUTATIVITY THEOREMS CONCERNING ADDITIVE MAPPINGS AND DERIVATIONS ON SEMIPRIME RINGS

被引:0
|
作者
Ali, Shakir [2 ]
Dhara, Basudeb [3 ]
Fosner, Ajda [1 ]
机构
[1] Univ Primorska, Fac Management, Cankarjeva 5, SI-6104 Koper, Slovenia
[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India
[3] Belda Coll, Dept Math, Paschim Medimpur 721424, India
关键词
Prime ring; semiprime ring; ideal; derivation; generalized derivation; GENERALIZED DERIVATIONS; CENTRALIZING MAPPINGS; PRIME-RINGS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let R be a ring with its center Z(R) and I a nonzero ideal of R. The purpose of this paper is to investigate identities satisfied by additive mappings on prime and semiprime rings. More precisely, we prove the following result. Let R be a semiprime ring, and let F, d : R -> R be two additive mappings such that F(xy) = F(x)y + xd(y) for all x, y is an element of R. If F(xy) +/- xy is an element of Z(R) for all x, y is an element of I, then [d(x), x] = 0 for all x is an element of I. Further, if d is a derivation such that d(I) not equal (0), then R contains a nonzero central ideal. Moreover, if R is prime and d is a derivation such that d(I) not equal (0), then R is commutative.
引用
收藏
页码:135 / 143
页数:9
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