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On a class of rings of order \(p^5\). (English) Zbl 1055.16023

Finite rings form a class of rings which many ring theorists are studying. This paper describes all rings of order \(p^5\), of a certain class of finite rings which satisfy the conditions (1) the set of all zero-divisors forms an ideal \(M\); (2) \(M^3=0\); and (3) \(M^2\neq 0\).

MSC:

16P10 Finite rings and finite-dimensional associative algebras
13M05 Structure of finite commutative rings
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