Serial rings and subdirect products
type: Item
instance of: scholarly article
title: Serial rings and subdirect products
zbMATH Open document ID: 0531.16017
DOI: 10.1016/0022-4049(83)90052-X
author: Joel K. Haack
published in: Journal of Pure and Applied Algebra
publication date: 1983-01-01T00:00:00Z
review text: Let R be an indecomposable basic generalized uniserial ring. Then R is a subdirect product of factor rings of (S,M)-triangular matrix rings, where S is a local uniserial ring and \(M=rad S\). The author also shows that in the special case, when R is a subdirect product of (S,M)-triangular matrix rings, R has a selfduality. A more general result, however, is true. It was already stated by \textit{I. Amdal} and \textit{F. Ringdal} [C.R. Acad. Sci., Paris, Sér. A 267, 85-87, 247-249 (1968; Zbl 0159.022)] and has recently been proved independently by \textit{W. Müller}, \textit{F. Dischinger} [Arch. Math. (to appear); Zbl 0532.16014)] and by J. Waschbüsch, that every generalized uniserial ring has a selfduality.
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16Gxx
Mathematics Subject Classification ID: 16P20
zbMATH DE Number: 3842081
zbMATH Keywords: triangular matrix rings
zbMATH Keywords: selfduality
reviewed by: Herbert Kupisch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3842081