When the annihilator graph of a commutative ring is planar or toroidal?

  • Moharram Bakhtyiari K.N. Toosi University of Technology
  • Reza Nikandish Jundi-Shapur University of Technology
  • Mohammad Javad Nikmehr K.N. Toosi University of Technology
Keywords: Annihilator graph, planarity, toroidality

Abstract

Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. The annihilator graph of R is defined as the undirected graph AG(R) with the vertex set Z(R)* = Z(R) \ {0}, and two distinct vertices x and y are adjacent if and only if  ann_R(xy) \neq ann_R(x) \cup ann_R(y). In this paper, all rings whose annihilator graphs can be embedded on the plane or torus are classified.

Author Biographies

Moharram Bakhtyiari, K.N. Toosi University of Technology

Faculty of Mathematics

Reza Nikandish, Jundi-Shapur University of Technology

Department of Mathematics

Mohammad Javad Nikmehr, K.N. Toosi University of Technology

Faculty of Mathematics

Published
2020-12-31
Section
Articles