Abstract
Let R be a 2-torsion free prime ring containing a non-trivial idempotent and R ′ be an arbitrary ring. Suppose that M: R → R ′ and M * : R ′ → R are surjective maps such that M(xM * (y)x)=M(x)yM(x), M * (yM(x)y)=M * (y)xM * (y) for all x∈ R , y∈ R ′ . Then both M and M * are additive. In particular, a bijective map φ: R → R ′ satisfying φ ( xyx )= φ ( x ) φ ( y ) φ ( x ) for all x,y∈ R is additive.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
