Abstract:
Let M be a Γ-ring. An element a∈M is called a dependent element on a mapping F: M→M if F(x)αa = aαx holds for all x∈M, α∈Γ. In this study, we determine the characterizations of dependent elements on certain mappings on prime and semiprime Γ-rings by taking a certain assumption xαyβz = xβyαz for all x,y,z∈M, α,β∈Γ. For the case of semiprime Γ-ring M, we also prove that the mapping σ+τ is a free action if σ and τ are automorphisms of M.
Kalyan Kumar Dey, Akhil Chandra Paul and Isamiddin S. Rakhimov, 2012. Dependent Elements in Prime and Semiprime Gamma Rings. Asian Journal of Algebra, 5: 11-20.
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