Abstract
Let be a semiprime ring, a nonzero ideal of , and , two epimorphisms of . An additive mapping is generalized -derivation on if there exists a -derivation such that holds for all . In this paper, it is shown that if , then contains a nonzero central ideal of , if one of the following holds: (i) ; (ii) ; (iii) ; (iv) ; (v) for all .
Highlights
Throughout the present paper, R always denotes an associative semiprime ring with center Z R
An additive mapping F : R → R is generalized σ, τ -derivation on R if there exists a σ, τ -derivation d : R → R such that F xy Fxσyτxdy holds for all x, y ∈ R
An additive mapping d : R → R is said to be derivation if d xy d x y xd y holds for all x, y ∈ R
Summary
Let R be a semiprime ring, I a nonzero ideal of R, and σ, τ two epimorphisms of R. An additive mapping F : R → R is generalized σ, τ -derivation on R if there exists a σ, τ -derivation d : R → R such that F xy Fxσyτxdy holds for all x, y ∈ R. It is shown that if τ I d I / 0, R contains a nonzero central ideal of R, if one of the following holds: i F x, y.
Sign-in/Register to view highlights & summary 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.
