Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GAS-module and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P*); (3) R is semilocal if and only if every cyclic module is a GWS-module.
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Wang et al. (2006) studied this question.