POWER CHAINS IN A DIVISOR GRAPH
Journal Title: IMPACT : International Journal of Research in Humanities, Arts and Literature ( IMPACT : IJRHAL ) - Year 2019, Vol 7, Issue 4
Abstract
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.
Authors and Affiliations
SATYANARAYANA BHAVANARI, SRINIVASULU DEVANABOINA, Mallikarjuna Bhavanari, Abul Basar
Keywords
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