Finite rings of order
where
have previously been completely classified up to isomorphism. Given a finite local ring
of order
and characteristic
with Jacobson
radical
,
for
some
.
For
,
. In this paper, local
rings of order
with
are completely classified. Furthermore,
for
, chain rings are classified fully. Many
of the remaining cases are also completed. For some of the incomplete cases, techniques for solving them are outlined.
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