An annotation on the prime graph of  an integral domain

Mohiddin Shaw Shaik 1 *, Nagaraju Dasari 2 and Neha Gahlot 3

doi:10.26637/MJM0803/0025

An annotation on the prime graph of an integral domain

Authors :

Mohiddin Shaw Shaik ^{1 *}, Nagaraju Dasari ² and Neha Gahlot ³

Author Address :

¹ Department of Mathematics, Narasaraopeta Engineering College, Narasaraopet-522601, Andhra Pradesh, India.
^2,3Department of Mathematics and Statistics, Manipal University, Jaipur-303007, Rajasthan, India.

*Corresponding author.

Abstract :

We introduce the prime graph of the product ring $R_{1}$ $\times R_{2}$ where $R_{1}$, $R_{2}$ are integral domains, which is an extension of study on prime graph of an integral domain. We prove that, if $R_{1}, R_{2}$ are two integral domains, the graph obtained by removing the isolated vertices from PG($R_{1}$ $\times R_{2}$) is a bipartite graph. We obtain some consequences.

Keywords :

Associative ring, Integral Domain, Graph, Prime Graph.

DOI :

10.26637/MJM0803/0025

Article Info :

Received : February 02, 2020; Accepted : May 22, 2020.