Some Commutativity Theorems for Near-Rings with Left Multipliers

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DOI: 10.46793/KgJMat2002.205B


Let ???? be a 3-prime near-ring with the center Z(????), and U be a nonzero semigroup ideal of ????. In the present paper it is shown that a 3-prime near-ring ???? is a commutative ring if and only if it admits left multipliers and G satisfying any one of the following properties: (i)(x)G(y) ± [x,y] Z(????); (ii)(x)G(y) ± x y Z(????); (iii)(x)G(y) ± yx Z(????); (iv)(x)G(y) ± xy Z(????) and (v)([x,y]) ± G(x y) Z(????) for all x,y U.


3-Prime near-ring, derivations, commutativity, generalized derivation, left multiplier.


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