Abstract:
The study of finite extension of Galois rings in the recent past have given rise to commutative
completely primary finite rings that have attracted much attention as they have yielded important results towards
classification of finite rings into well-known structures. In this paper, we give a construction of a class of completely
primary finite ring R of characteristic p whose subsets of zero divisors ( ) Z R satisfy the condition
( ) ( ) ( ) ( ) ( ) ( ) 6 5 0 ; 0 Z R Z R = . The ring R is constructed over its subring ( ) 0
,r R GR p p = as an
idealization of the 0
R- modules. A thorough determination and classification of the structure of the group of
invertible elements using fundamental theorem of finitely generated abelian groups is given.
