Commutative rings whose certain modules decompose into direct sums of cyclic submodules

Farid Kourki; Rachid Tribak

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 4, page 1099-1117
  • ISSN: 0011-4642

Abstract

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We provide some characterizations of rings R for which every (finitely generated) module belonging to a class 𝒞 of R -modules is a direct sum of cyclic submodules. We focus on the cases, where the class 𝒞 is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.

How to cite

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Kourki, Farid, and Tribak, Rachid. "Commutative rings whose certain modules decompose into direct sums of cyclic submodules." Czechoslovak Mathematical Journal 73.4 (2023): 1099-1117. <http://eudml.org/doc/299367>.

@article{Kourki2023,
abstract = {We provide some characterizations of rings $R$ for which every (finitely generated) module belonging to a class $\mathcal \{C\}$ of $R$-modules is a direct sum of cyclic submodules. We focus on the cases, where the class $\mathcal \{C\}$ is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.},
author = {Kourki, Farid, Tribak, Rachid},
journal = {Czechoslovak Mathematical Journal},
keywords = {decomposition of a module; FGC-ring; Köthe ring; semiartinian module; (semi-)V-module; locally supplemented module},
language = {eng},
number = {4},
pages = {1099-1117},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Commutative rings whose certain modules decompose into direct sums of cyclic submodules},
url = {http://eudml.org/doc/299367},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Kourki, Farid
AU - Tribak, Rachid
TI - Commutative rings whose certain modules decompose into direct sums of cyclic submodules
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1099
EP - 1117
AB - We provide some characterizations of rings $R$ for which every (finitely generated) module belonging to a class $\mathcal {C}$ of $R$-modules is a direct sum of cyclic submodules. We focus on the cases, where the class $\mathcal {C}$ is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.
LA - eng
KW - decomposition of a module; FGC-ring; Köthe ring; semiartinian module; (semi-)V-module; locally supplemented module
UR - http://eudml.org/doc/299367
ER -

References

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