Automorphims of Zero Divisor Graphs of Galois Rings

Abstract

Let Rbe a commutative finite ring with unity and let Z(R) be itsset of zero divisors. The study of Rin which the subset of zero divi-sors forms a unique maximal ideal has been extensively done yieldinginteresting and useful results. For different classes of R, the invert-ible element have been characterized by use of fundamental theorem offinitely generated abelian groups while Z(R) has been characterized viathe zero divisor graphs. Scanty in the literature are the maps that pre-serve the structures of Rand its subsets. In this paper we discover andcharacterize the automorphisms of zero divisor graphs of Galois rings.