Abstract:
Let Ro be a Galois ring. It is well known that every element of Ro is either a
zero divisor or a unit. Galois rings are building blocks of completely primary
finite rings which have yielded interesting results towards classification of
finite rings. Recent studies have revealed that every finite commutative ring
is a direct sum of completely primary finite rings. In fact, extensive account
of finite rings have been given in the recent past. However, the classification
of finite rings into well known structures still remains an open problem. For
instance, the structure of the group of units of Ro is known and some results
have been obtained on the structure of its zero divisor graphs. In this paper,
we construct a finite extension of Ro (a special class of completely primary
finite rings) and classify its group of units for all the characteristics.
