The Diameter of a Zero-Divisor Graph for Finite Direct Product of Commutative Rings

Authors

  • S. Ebrahimi Atani Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran
  • M. Shajari Kohan Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran

DOI:

https://doi.org/10.5644/SJM.03.2.01

Keywords:

Zero-divisor graph, diameter, finite direct product

Abstract

This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product
$R_{1}\times R_{2}\times\cdots\times R_{n}$ with respect to the diameters of the zero-divisor graphs of $R_{1},R_{2},\cdots,R_{n-1}$ and $R_{n}(n>2).$

 

2000 Mathematics Subject Classification. 05C75, 13A15

Downloads

Download data is not yet available.

References

D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217 (1999), 434–447.

I. Beck, Coloring of commutative rings, J. Algebra, 116 (1988), 208–226.

T. G. Lucas, The diameter of a zero-divisor graph, J. Algebra, 301 (2006), 174–193.

S. P. Remond, An ideal-based zero-divisor graph of a commutative ring, Commun. Algebra, 31 (2003), 4425–4443.

J. Warfel, Zero divisor graphs for direct product of commutative rings, Huston J. Mathematics, to appear.

Downloads

Published

12.06.2024

How to Cite

Atani, S. E., & Kohan, M. S. (2024). The Diameter of a Zero-Divisor Graph for Finite Direct Product of Commutative Rings. Sarajevo Journal of Mathematics, 3(2), 149–156. https://doi.org/10.5644/SJM.03.2.01

Issue

Section

Articles