We study the class, STAR , of all *-modules by means of the classes, Sλ, of all *λ-modules, λ> 0 being a cardinal. Since STAR, equals the intersection of the decreasing chain Sλ, λ > 0, our approach 'from above' complements the usual approach 'from below' consisting in the study of quasi-progenerators and tilting modules. We present relations between categorical properties of *-;modules and those of *-modules. Answering a question of Menini, we use the solution of the Artin's problem to show that the chain Sλ,λ > No, is strictly decreasing in general.
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