On commutativity of completely prime gamma-rings - Rakhimov, Isamiddin Sattarovich; Dey, Kalyan Kumar; Paul, Akhil Chandra (Universiti Putra Malaysia Press, 2013)
In this paper we prove that any completely prime Γ -ring M satisfying the condition aαbβc=aβbαc = ( a,b,c ∈ M and α, β∈Γ )with nonzero derivation, is a commutative integral Γ -domain if its characteristic is not two. We also show that if the characteristic of M is 2 the Γ -ring M is either commutative or is an order in a simple 4-dimensional algebra over its center. We give necessary condition in terms of derivations for belongings of an element of the Γ -ring M to the center of M when the characteristic of M is not two. If char M = 2, and a Z M ∉ ( ), then we show that the derivation is the inner derivation.