Nous caractérisons les extensions triviales semiGoldie, de cogénération finie, mininjectives et quasi-Frobeniusiens. Comme application, nous montrons que tout anneau noethérien s’injecte dans un anneau quasi-Frobeniusien.
We prove that for a commutative ring , every noetherian (artinian) -module is quasi-injective if and only if every noetherian (artinian) -module is quasi-projective if and only if the class of noetherian (artinian) -modules is socle-fine if and only if the class of noetherian (artinian) -modules is radical-fine if and only if every maximal ideal of is idempotent.
We provide some characterizations of rings for which every (finitely generated) module belonging to a class of -modules is a direct sum of cyclic submodules. We focus on the cases, where the class 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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