Double Reverse Theta *- Centralizer of Rings With Involution

Ikram A. Saed

Abstract


Let  R be a ring  with involution  and  q  is a mapping  of R .It was known  that every double reverse   q- centralizer  is a double Jordan q*- centralizer  on  R but the converse  need  not  be  true . In  this  paper  we give  conditions  to  the converse  to be true .

Keywords


*- ring ; semiprime *- ring ; reverse *- centralizer ; involution ; double reverse *- centralizer ; double Jordan *- centralizer .

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References


Herstein , I.N.(1969).Topics in Ring Theory , University of Chicago Press , Chicago .

Herstein , I.N.(1976). Rings with Involution , University of Chicago Press , Chicago .

Fadhl , F.A.(2010) . Double Centralizers on Prime and Semiprime Rings . Baghdad University (Iraq). MSC. Thesis .

Obaid , A.A.(2009) . Additive Mappings on Prime and Semiprime Rings with Involution . Baghdad University (Iraq) . MSC. Thesis .

Ashraf , M . and Mozumder , M . R .(2012) . On Jordan α*- Centralizers in Semiprime Rings with Involution . Int. J. Contemp . Math. Sciences , 7(23), 1103-1112.


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