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Sur les Extensions Triviales Commutatives

Farid Kourki — 2009

Annales mathématiques Blaise Pascal

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.

On commutative rings whose maximal ideals are idempotent

Farid KourkiRachid Tribak — 2019

Commentationes Mathematicae Universitatis Carolinae

We prove that for a commutative ring R , every noetherian (artinian) R -module is quasi-injective if and only if every noetherian (artinian) R -module is quasi-projective if and only if the class of noetherian (artinian) R -modules is socle-fine if and only if the class of noetherian (artinian) R -modules is radical-fine if and only if every maximal ideal of R is idempotent.

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

Farid KourkiRachid Tribak — 2023

Czechoslovak Mathematical Journal

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.

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