Anti-automorphisms satisfying an Engel condition. Issue 9 (2nd September 2017)

• Record Type: Journal Article
• Authors: Lee, Tsiu-Kwen
• Is Part Of: Communications in algebra. Volume 45:Issue 9(2017)
• Page Start: 4030
• Page End: 4036
• Publication Date: 2017-09-02
• Subjects: Anti-automorphism -- commuting map -- Engel condition -- involution -- m-power commuting map -- semiprime ring; 16N60 -- 16R50; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1255894
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let R be a semiprime ring with an anti-automorphism τ, which is of finite order. It is proved that if[ [ … [ τ ( x ), x n 1 ], … ], x n k ] = 0 for all x ∈ R, wheren 1, n 2, …, n k are k fixed positive integers, then τ is a commuting map. Moreover, commuting anti-automorphisms of semiprime rings are also characterized.