### Abstract:

Let r be a positive integer and 2 ≤ ∈k . Let ( ) kr k GR p p, be a Galois ring of order kr p and
characteristic k p . Consider, ( ) kr k R GR p p U = ,⊕ where U is a finitely generated ( ) kr k GR p p,
module. If Z R( ) is the set of zero divisors in R satisfying the condition 2 ( ( )) ( ) kr r Z R GR p p ⊆ ,
then it is well known that R is a completely primary finite ring and the structure of its group of units
has been studied before. In this paper, we study the structure of its zero divisors via the zero divisor
graphs.