Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 584-592 |
| Number of pages | 9 |
| Journal | Canadian Mathematical Bulletin |
| Volume | 56 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2013 Sep 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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On automorphisms and commutativity in semiprime rings. / Liau, Pao Kuei; Liu, Cheng-Kai.
In: Canadian Mathematical Bulletin, Vol. 56, No. 3, 01.09.2013, p. 584-592.Research output: Contribution to journal › Article
TY - JOUR
T1 - On automorphisms and commutativity in semiprime rings
AU - Liau, Pao Kuei
AU - Liu, Cheng-Kai
PY - 2013/9/1
Y1 - 2013/9/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84880960187&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84880960187&partnerID=8YFLogxK
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 -