NILPOTENT FINITE RINGS WITH PLANAR ZERO-DIVISOR GRAPHS-Reference-Cited by-同舟云学术

NILPOTENT FINITE RINGS WITH PLANAR ZERO-DIVISOR GRAPHS

Published:2008-12 Issue:04 Volume:01 Page:565-574
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

KUZ'MINA A. S.¹,MALTSEV Yu. N.²

Affiliation:

1. Department of Mathematics, Barnaul State Pedagogical University, 55, Molodezhnaya St., Barnaul, 656031, Russia

2. Department of Mathematics, Altai State University, 61, Lenin St., Barnaul, 656099, Russia

Abstract

The zero-divisor graph Γ(R) of an associative ring R is the graph with all vertices non-zero zero-divisors (one-sided and two-sided) of R, and two distinct vertices x and y are joined by an edge iff xy = 0 or yx = 0 ([10]). In the present paper, we describe all nilpotent finite rings with planar zero-divisor graphs.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179355710800045X

Reference9 articles.

1. When a zero-divisor graph is planar or a complete r-partite graph

2. On zero-divisor graphs of finite rings

3. The Zero-Divisor Graph of a Commutative Ring

4. Coloring of commutative rings

5. Planar zero-divisor graphs

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