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Dependent Elements in Prime and Semiprime Gamma Rings

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Author(s): Kalyan Kumar Dey | Akhil Chandra Paul | Isamiddin S. Rakhimov

Journal: Asian Journal of Algebra
ISSN 1994-540x

Volume: 5;
Issue: 1;
Start page: 11;
Date: 2012;
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Keywords: Derivation | free action

ABSTRACT
Let M be a G-ring. An element a?M is called a dependent element on a mapping F: M?M if F(x)aa = aax holds for all x?M, a?G. In this study, we determine the characterizations of dependent elements on certain mappings on prime and semiprime G-rings by taking a certain assumption xayz = xyaz for all x,y,z?M, a,?G. For the case of semiprime G-ring M, we also prove that the mapping s+t is a free action if s and t are automorphisms of M.
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