CLASSES OF GENERALIZED ASTERISK-MODULES

We study the class, STAR, of all -modules by means of the classes, S( lambda), of all lambda-modules, lambda > 0 being a cardinal. Since ST AR equals the intersection of the decreasing chain S(lambda), lambda > 0, our approach ''from above'' complements the usual approach ''from below'' consisting in the study of quasi-progenerators and tilting mod ules. We present relations between categorical properties of lambda-m odules and those of -modules. Answering a question of Menini, we use the solution of the Artin's problem to show that the chain S(lambda), lambda > aleph 0, is strictly decreasing in general.