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2013 (Vol. 6, Issue: 22)
Article Information:

The &theta-Centralizers of Semiprime Gamma Rings

M.F. Hoque, H.O. Roshid and A.C. Paul
Corresponding Author:  M.F. Hoque 

Key words:  Centralizer, &theta-centralizer, Jordan centralizer, Jordan &theta-centralizer , left centralizer, left &theta-centralizer, semiprime Γ-ring
Vol. 6 , (22): 4129-4137
Submitted Accepted Published
November 19, 2012 May 07, 2013 December 05, 2013

Let M be a 2-torsion free semiprime Γ-ring satisfying a certain assumption and θ be an endomorphism of M. Let T:&rarrM be an additive mapping such that T(x&alphay&betax) = &theta(x)&alphaT(y)&beta&theta(x) holds for all x,y&isinM and α,β&isinΓ. Then we prove that T is a &theta-centralizer. We also show that T is a &theta-centralizer if M contains a multiplicative identity 1. 2010 Mathematics Subject Classification, Primary 16N60, Secondary 16W25, 16U80.
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  Cite this Reference:
M.F. Hoque, H.O. Roshid and A.C. Paul, 2013. The &theta-Centralizers of Semiprime Gamma Rings.  Research Journal of Applied Sciences, Engineering and Technology, 6(22): 4129-4137.
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