Extensions of uniserial modules

Gabriella D'Este; Fatma Kaynarca; Derya Keskin Tütüncü

doi:10.4171/rsmup/57

JournalsrsmupVol. 144pp. 73–86

Extensions of uniserial modules

Gabriella D'Este
Università degli Studi di Milano, Italy
Fatma Kaynarca
University of Afyon Kocatepe, Afyonkarahisar, Turkey
Derya Keskin Tütüncü
Hacettepe University, Beytepe, Ankara, Turkey

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Abstract

Let $R$ be any ring and let $0 \to A \to B \to C \to 0$ be an exact sequence of $R$ -modules which does not split with $A$ and $C$ uniserial. Then either $B$ is indecomposable or $B$ has a decomposition of the form $B = B_{1} \oplus B_{2}$ where $B_{1}$ and $B_{2}$ are indecomposable and at least one of them is uniserial.

Cite this article

Gabriella D'Este, Fatma Kaynarca, Derya Keskin Tütüncü, Extensions of uniserial modules. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 73–86

DOI 10.4171/RSMUP/57