NONCOMMUTATIVE RINGS OF ORDER P(4)

Every finite ring can be written as a direct sum of rings which have p rime power orders. Consequently, questions about finite rings often re duce to questions about rings with order p(n) for some prime p. This p aper describes all the isomorphism classes of noncommutative rings wit h unity and order p4. It is shown that for an odd prime p there are p + 8 distinct classes of rings with characteristic p and p + 4 classes for characteristic p2. For p = 2 there are 9 classes for characteristi c 2 and 4 classes for characteristic 4.