POWER CHAINS IN A DIVISOR GRAPH

The divisor graph of an associative ring R (denoted as DG(R)) was introduced by Satyanarayana, Srinivasulu.[9]. In this paper, we introduce a simple concept “Power Chain in a Divisor Graph” .We prove that if is nilpotent, then the power chain starting with a is of finite length. If DG(R) (the divisor graph of R) contains a power chain starting with which is of infinite length, then , a is non–idempotent and non–nilpotent element. We announce some basic results. Finally, we deduce that if R be an integral domain and a , then if and only if the power chain starting with a (in DG(R)) is of infinite length.