Einreihig zerlegbare Ringe sind selbstdual
type: Item
instance of: scholarly article
title: Einreihig zerlegbare Ringe sind selbstdual
zbMATH Open document ID: 0532.16014
DOI: 10.1007/BF01193910
author: F. Dischinger
author: W. Müller
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: We show in this paper that every serial ring has a weakly symmetric self- duality: If \(e_ 1,...,e_ n\) is a full set of orthogonal primitive idempotents in the basic serial ring \(R\), then \(S=\sum^{n}_{i=1}e_ iRe_ i\) is a QF-subring of \(R\) and \(_ SU_ R=\Hom_ S(R_ S,U_ S)\) is the minimal injective right \(R\)-cogenerator. The proof of the theorem consists in extending the left module-structure from \(S\) to \(R\). Recently we learned from J. Waschbüsch that the above assertion can be found without proof in the article of \textit{I. K. Amdal} and \textit{F. Ringdal} [C. R. Acad. Sci., Paris, Sér. A 267, 247-249 (1968; Zbl 0159.02201)].
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 16Gxx
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16U99
zbMATH DE Number: 3843947
zbMATH Keywords: minimal injective right cogenerator
zbMATH Keywords: serial ring
zbMATH Keywords: weakly symmetric self- duality
zbMATH Keywords: orthogonal primitive idempotents
zbMATH Keywords: basic serial ring
MaRDI profile type: Publication
cites work: Duality for semigroup rings
cites work: Self-duality and serial rings
full work available at URL: https://doi.org/10.1007/bf01193910
OpenAlex ID: W1976909637
description: scientific article; zbMATH DE number 3843947