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

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Abstract

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

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Authors and Affiliations

  1. Equipe de Recherche: Algèbre & Didactique des Mathématiques, Centre Régional des Métiers de l’Education et de la Formation de la Région Tanger-Tétouan-Al Hoceima, (CRMEF-TTH)-Tanger, Avenue My Abdelaziz, Souani, BP: 3117, Tangier, Morocco

    Farid Kourki & Rachid Tribak

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  1. Farid Kourki
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  2. Rachid Tribak
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Correspondence to Rachid Tribak.

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Kourki, F., Tribak, R. Commutative rings whose certain modules decompose into direct sums of cyclic submodules. Czech Math J 73, 1099–1117 (2023). https://doi.org/10.21136/CMJ.2023.0392-22

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