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Keywords:
decomposition of a module; FGC-ring; Köthe ring; semiartinian module; \hbox {(semi-)V-module}; locally supplemented module
decomposition of a module; FGC-ring; Köthe ring; semiartinian module; \hbox {(semi-)V-module}; locally supplemented module
Summary:
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.
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