-CENTRALIZING MAPPINGS OF SEMIPRIME -RINGS

Abdulrahman  Majeed; Sameer  Motashar

doi:10.24996/

Authors

Abdulrahman Majeed Department of Mathematics , College of Sciences , University of Baghdad. Baghdad-Iraq
Sameer Motashar Department of Mathematics , College of Sciences , University of Baghdad. Baghdad-Iraq

DOI:

https://doi.org/10.24996/

Keywords:

-Ring,Derevitions, , -centralizing, , prim -ring , , semi-prim -ring.

Abstract

Let M be a -Ring with center Z(M) and S a non-empty subset of M. A mapping F from M to M is called -centralizing on S if [x,F(x)]α= xαF(x)-F(x)αxZ(M) for all xS,α . we show that a semi-prime Γ-ring M must have a non-trivial central ideal if it admits an endomorphism which is Γ-centralizing on some non-trivial one –sided ideal.