Classification of not commutative rings with identity of order dividing \(p^ 4\)
The authors indicate that the investigation of the paper has been inspired by the question posed by them [in Indag. Math., New Ser. 3, No. 1, 11-26 (1992; Zbl 0771.16009)]: ``Do there exist local rings with one minimal left but more than one minimal right ideal?'' Let \(R\) be a ring mentioned in the title and \(J\) its Jacobson radical. The concluding classification table numbers 15 types of mutually non-isomorphic indecomposable rings \(R\) and points out the height \(h\), a base \(B_R\) for \(R^+\), a base \(B_J\) for \(J^+\), the non-zero, non-trivial products of basic elements of \(R^+\) for each type of rings and, in view of the above question, the type of rings anti-isomorphic to the type under consideration, if existent. The initial point for the investigation is the classification of nilpotent rings of orders dividing \(p^3\) borrowed from \textit{R. Kruse} and \textit{D. Price} [Nilpotent rings (1969; Zbl 0198.361)].
scientific article; zbMATH DE number 792823