Research Article | OPEN ACCESS
The &theta-Centralizers of Semiprime Gamma Rings
1M.F. Hoque, 1H.O. Roshid and 2A.C. Paul
1Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh
2Department of Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh
Research Journal of Applied Sciences, Engineering and Technology 2013 22:4129-4137
Received: November 19, 2012 | Accepted: May 07, 2013 | Published: December 05, 2013
Abstract
Let M be a 2-torsion free semiprime Γ-ring satisfying a certain assumption and θ be an endomorphism of M. Let T: M→M be an additive mapping such that T(x&alphay&betax) = &theta(x)&alphaT(y)&beta&theta(x) holds for all x, y∈ M and &alpha, &beta∈Γ. 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.
Keywords:
Centralizer, &theta-centralizer, Jordan centralizer, Jordan &theta-centralizer, left centralizer, left &theta-centralizer, semiprime &Gamma-ring,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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