COMMUTATIVITY AND DECOMPOSITION FOR NEAR RINGS
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Abstract
Let $R$ be a distributively generated (d.g) near ring satisfy one of the following condit ions.
(*) For each $x$, $y$ in $R$, there exists a positive integer $n =n(x,y)$ such that $xy =(yx)^n$.
(**) For each $x$, $y$ in $R$, there exist positive integers $m = m(x,y)$ and $n = n(x,y)$ for which $xy = y^m x^n$.
In [2], Bell proved the commutativity of $R$ satisfying (*) or (**) under appropriate additional hypothesis. In this paper, we generalize the above properties for wider class of near rings known as D-near rings. Also we provide an example for justification of our results. Furthermore, we give a decomposition Theorem for near rings satisfying (**).
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References
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