Anti-endomorphisms and endomorphisms satisfying an Engel condition. Issue 10 (3rd October 2019)

• Record Type: Journal Article
• Authors: Pınar Eroǧlu, Münevver; Lee, Tsiu-Kwen; Lin, Jheng-Huei
• Is Part Of: Communications in algebra. Volume 47:Issue 10(2019)
• Page Start: 3950
• Page End: 3957
• Publication Date: 2019-10-03
• Subjects: (Anti-)endomorphism -- Engel condition -- power commuting map -- semi-linear map -- semiprime ring -- prime ring; 16R60 -- 16N60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1572175
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be a semiprime ring with τ an anti-endomorphism or endomorphism. It is proved that if τ satisfies an Engel condition [ [ … [ [ x τ, x n 1 ], x n 2 ] … ], x n k ] = 0 for all x ∈ R, where n 1, n 2, …, n k are k fixed positive integers, then τ is a commuting map (i.e. [ x τ, x ] = 0 for all x ∈ R ). The theorem generalizes the results proved in [22 ] with τ an anti-automorphism of finite order and in [10, 11 ] with R a division ring, respectively.