On Automorphisms and Commutativity in Semiprime Rings

被引:15
作者
Liau, Pao-Kuei [1 ]
Liu, Cheng-Kai [1 ]
机构
[1] Natl Changhua Univ Educ, Dept Math, Changhua 500, Taiwan
来源
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2013年 / 56卷 / 03期
关键词
semiprime ring; automorphism; generalized polynomial identity (GPI); ENGEL CONDITION; GENERALIZED DERIVATIONS; CENTRALIZING MAPPINGS; LIE IDEALS; DIFFERENTIAL IDENTITIES; PRIME-RINGS; SUBGROUPS; THEOREM;
D O I
10.4153/CMB-2011-185-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let R be a semiprime ring with center Z(R). For x, gamma is an element of R, we denote by [x,y] = xy - yx the commutator of x and y. If sigma is a non-identity automorphism of R such that [[ ... [[sigma(x(n0)), x(n1)], xn(2)], ... ], xn(k)] = 0 for all x is an element of R, where n(0), n(1), n(2), ... , n(k) are fixed positive integers, then there exists a map mu: R -> Z(R) such that sigma(x) = x + mu(x) for all x is an element of R. In particular, when R is a prime ring, R is commutative.
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页码:584 / 592
页数:9
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