On commutative rings whose maximal ideals are idempotent
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.