Let R be a ring and 3C a class of right J?-modules.Let M be a right JRmodule such that for every submodule N of M there exists a direct summand K of M such that Nc:K and K/N&3C.The structure of M is investigated in the cases that 3C consists of Noetherian right i?-modules, right Λ-modules with Krull dimension and right /?-modules with finite uniform dimension, respectively.
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Patrick F. Smith (1990) studied this question.