On automorphisms and commutativity in semiprime rings

Pao Kuei Liau, Cheng Kai Liu

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)584-592
Number of pages9
JournalCanadian Mathematical Bulletin
Issue number3
Publication statusPublished - 2013 Sep

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On automorphisms and commutativity in semiprime rings'. Together they form a unique fingerprint.

Cite this