Abstract:
Let J be the Jacobson radical of a commutative completely primary
finite ring R such that J
k 6= (0) and J
k+1 = (0). Then R/J ∼= GF(p
r
), the
finite field of p
r
elements, and the characteristic of R is p
k where k ≥ 2 and p is
some prime integer. In this paper, we determine the structures of the quotient
groups 1 + J
i/1 + J
i+1 for every characteristic of R and 1 ≤ i ≤ k − 1.
