Extensions of uniserial modules

Gabriella D’este; Fatma Kaynarca; Derya Keskin Tütüncü

doi:10.4171/RSMUP/57

Extensions of uniserial modules

Gabriella D’este
, Fatma Kaynarca
, Derya Keskin Tütüncü

Division of Algebra and Number Theory

Research output: Contribution to journal › Article › peer-review

Abstract

– Let R be any ring and let 0 → A → B → C → 0 be an exact sequence of R-modules which does not split with A and C uniserial. Then either B is indecom-posable or B has a decomposition of the form B = B₁ ⊕ B₂ where B₁ and B₂ are indecomposable and at least one of them is uniserial.

Original language	English
Pages (from-to)	73-86
Number of pages	14
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	144
DOIs	https://doi.org/10.4171/RSMUP/57
Publication status	Published - 2020

Keywords

Hollow modules
Quivers and represen-tations
Uniform modules
Uniserial modules

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title = "Extensions of uniserial modules",

abstract = "– Let R be any ring and let 0 → A → B → C → 0 be an exact sequence of R-modules which does not split with A and C uniserial. Then either B is indecom-posable or B has a decomposition of the form B = B1 ⊕ B2 where B1 and B2 are indecomposable and at least one of them is uniserial.",

keywords = "Hollow modules, Quivers and represen-tations, Uniform modules, Uniserial modules",

author = "Gabriella D{\textquoteright}este and Fatma Kaynarca and T{\"u}t{\"u}nc{\"u}, \{Derya Keskin\}",

year = "2020",

doi = "10.4171/RSMUP/57",

language = "English",

volume = "144",

pages = "73--86",

journal = "Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova",

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AU - D’este, Gabriella

AU - Kaynarca, Fatma

AU - Tütüncü, Derya Keskin

PY - 2020

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N2 - – Let R be any ring and let 0 → A → B → C → 0 be an exact sequence of R-modules which does not split with A and C uniserial. Then either B is indecom-posable or B has a decomposition of the form B = B1 ⊕ B2 where B1 and B2 are indecomposable and at least one of them is uniserial.

AB - – Let R be any ring and let 0 → A → B → C → 0 be an exact sequence of R-modules which does not split with A and C uniserial. Then either B is indecom-posable or B has a decomposition of the form B = B1 ⊕ B2 where B1 and B2 are indecomposable and at least one of them is uniserial.

KW - Hollow modules

KW - Quivers and represen-tations

KW - Uniform modules

KW - Uniserial modules

UR - https://www.scopus.com/pages/publications/85097608260

U2 - 10.4171/RSMUP/57

DO - 10.4171/RSMUP/57

M3 - Article

AN - SCOPUS:85097608260

SN - 0041-8994

VL - 144

SP - 73

EP - 86

JO - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

JF - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

ER -

Extensions of uniserial modules

Abstract

Keywords

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