An annotation on the prime graph of an integral domain

Mohiddin Shaw Shaik; Nagaraju Dasari; Neha Gahlot

doi:10.26637/MJM0803/0025

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 $\mathrm{PG}\left(R_1 \times R_2\right)$ is a bipartite graph. We obtain some consequences.

Keywords:

Associative ring, Integral Domain, Graph, Prime Graph

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Mohiddin Shaw Shaik Department of Mathematics, Narasaraopeta Engineering College, Narasaraopet-522601, Andhra Pradesh, India.
Nagaraju Dasari Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur-303007, Rajasthan, India.
Neha Gahlot Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur-303007, Rajasthan, India.

Pages: 882-885
Date Published: 01-07-2020
Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

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