Einreihig zerlegbare Ringe sind selbstdual
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)].
scientific article; zbMATH DE number 3843947