Geodesic
On commutative rings whose maximal ideals are idempotent
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 3, pp. 313-322.

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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.
DOI : 10.14712/1213-7243.2019.012
Classification : 13C13, 13E05, 13E10, 13E99
Keywords: artinian module; modules of finite length; noetherian module; quasi-injective module; quasi-projective module; radical-fine class of modules; socle-fine class of modules 
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Kourki, Farid; Tribak, Rachid. On commutative rings whose maximal ideals are idempotent. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 3, pp. 313-322. doi : 10.14712/1213-7243.2019.012. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2019.012/

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