Abstract:
A ring is Galois if its subset of all the zero divisors (including zero)
forms a principal ideal. Galois rings are generalizations of Galois fields
and have been used widely in the past few decades to construct various
optimal families of error correcting codes. These rings are important
in the structure theory of finite commutative rings. Furthermore, Ga lois rings are the building blocks of Completely Primary Finite Rings
(C.P.F.R) which play a fundamental role in the study of the structures
of finite rings in the sense that every finite ring is expressible as a di rect sum of matrix rings over Completely Primary Finite Rings. Zero
divisor graphs have been of interest to Mathematicians, particularly in
understanding the structures of zero divisors in finite rings. However,
not much is known about the adjacency matrices of zero divisor graphs
of finite rings. In this paper we present some explicit results on the
adjacency matrices of the Anderson-Livingston zero divisor graphs of
Galois rings
