Classification of not commutative rings with identity of order dividing \(p^ 4\)
type: Item
instance of: scholarly article
title: Classification of not commutative rings with identity of order dividing \(p^ 4\)
zbMATH Open document ID: 0834.16017
DOI: 10.1016/0019-3577(95)91241-M
author: R. W. Goldbach
author: H. L. Claasen
published in: Indagationes Mathematicae. New Series
publication date: 1996-03-24T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 13M05
zbMATH DE Number: 792823
zbMATH Keywords: local rings
zbMATH Keywords: minimal right ideals
zbMATH Keywords: Jacobson radical
zbMATH Keywords: indecomposable rings
zbMATH Keywords: height
zbMATH Keywords: bases
zbMATH Keywords: products of basic elements
zbMATH Keywords: nilpotent rings
reviewed by: Feliks R. Bobovich
MaRDI profile type: Publication
cites work: A field-like property of finite rings
cites work: Q3958602
cites work: Enumerating Finite Rings
cites work: Q4046212
cites work: Q5538955
description: scientific article; zbMATH DE number 792823