ONE SIDED ZERO DIVISOR GRAPHS OF RINGS WITH A TOTAL ORDER

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Published: 2017-01-06

Page: 9-17


SATYANARAYANA BHAVANARI

Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar – 522 510, Andhra Pradesh, India.

SRINIVASULU DEVANABOINA *

Department of BSH, NRI Institute of Technology, Agiripalli‐ 521 212, Andhra Pradesh, India.

HYMAVATHI TALLA

Department of Mathematics, Adikavi Nannaya University, Rajamahendravaram – 533 296, Andhra Pradesh, India

MALLIKARJUN BHAVANARI

Department of Mechanical Engineering, Institute of Energy Engineering, National Central University, Zhongli District, Taoyuan- 32001, Taiwan, R.O.C

*Author to whom correspondence should be addressed.


Abstract

In this paper we consider prime graph of R (denoted by PG(R)) of an associative ring R (introduced by Satyanarayana, Syam Prasad and Nagaraju [1]). This short paper is divided into four Sections. Section-1 is devoted for preliminary definitions. In section-2, we constructed Right zero divisor graph of R (denoted by RZDG(R)) where R = the set of all 2×2 matrices over the ring Z_2 of integers modulo 2. In section-3, we proved some equivalent conditions related to one sided zero divisor graphs on rings with certain total order (which is not concern with the binary operations of the ring R) and compared with prime graph. Some related fundamental results were mentioned.

Keywords: Prime graph, zero divisor graph, left zero divisor graph of R, right zero divisor graph, star graph, associative ring


How to Cite

BHAVANARI, S., DEVANABOINA, S., TALLA, H., & BHAVANARI, M. (2017). ONE SIDED ZERO DIVISOR GRAPHS OF RINGS WITH A TOTAL ORDER. Asian Journal of Mathematics and Computer Research, 15(1), 9–17. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/698

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