TY - JOUR

T1 - On automorphisms and commutativity in semiprime rings

AU - Liau, Pao Kuei

AU - Liu, Cheng Kai

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/9

Y1 - 2013/9

N2 - Let R be a semiprime ring with center Z(R). For x; y 2 R, we denote by [x; y] = xy - yx the commutator of x and y. If is a non-identity automorphism of R such that ⋯ [(xn0 ); xn1 ]; xn2 ; ⋯ ; xnk = 0 for all x 2 R, where n0; n1; n2; ⋯ ; nk are fixed positive integers, then there exists a map : R ! Z(R) such that (x) = x + (x) for all x 2 R. In particular, when R is a prime ring, R is commutative.

AB - Let R be a semiprime ring with center Z(R). For x; y 2 R, we denote by [x; y] = xy - yx the commutator of x and y. If is a non-identity automorphism of R such that ⋯ [(xn0 ); xn1 ]; xn2 ; ⋯ ; xnk = 0 for all x 2 R, where n0; n1; n2; ⋯ ; nk are fixed positive integers, then there exists a map : R ! Z(R) such that (x) = x + (x) for all x 2 R. In particular, when R is a prime ring, R is commutative.

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U2 - 10.4153/CMB-2011-185-5

DO - 10.4153/CMB-2011-185-5

M3 - Article

AN - SCOPUS:84880960187

VL - 56

SP - 584

EP - 592

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 3

ER -