Semi-perfect semi-distributive rings
type: Item
instance of: scholarly article
title: Semi-perfect semi-distributive rings
zbMATH Open document ID: 0958.16019
DOI: 10.1023/A:1009969911772
published in: Algebras and Representation Theory
publication date: 2001-04-02T00:00:00Z
review text: This article contains a series of results on semi-perfect semi-distributive rings (SPSD-rings) and on some specializations, using the concepts of quiver and prime quiver of such rings. In the introductory part (\S 1) some characterizations of semi-perfect rings are shown and conditions when such rings are semi-distributive are mentioned. The following part (\S 2) is devoted to the study of Noetherian SPSD-rings, describing the form of the associated quivers. The intersection of all natural powers of the Jacobson radical \(R\) of a Noetherian SPSD-ring \(A\) is zero. In the last part (\S 3) the hereditary and semi-hereditary SPSD-rings are investigated, reducing their description to the case of prime semi-hereditary serial rings. For such rings the existence and the form of classical quotient rings is shown.
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16E60
zbMATH DE Number: 1475287
zbMATH Keywords: semi-perfect semi-distributive rings
zbMATH Keywords: prime quivers
zbMATH Keywords: Noetherian SPSD-rings
zbMATH Keywords: semi-hereditary SPSD-rings
zbMATH Keywords: prime semi-hereditary serial rings
zbMATH Keywords: quotient rings
author: V. V. Kirichenko
reviewed by: A. I. Kashu
MaRDI profile type: Publication
full work available at URL: a:1009969911772
OpenAlex ID: W44000696
description: scientific article; zbMATH DE number 1475287