Let M be a right R-module. M is called H-supplemented if for a submodule A of M there exists a direct summand D of M such that M = A + X holds if and only if M = D + X. Let M = M1 ⊕ M2 be a duo module. Then M is H-supplemented if and only if M1 and M2 are H-supplemented modules.
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Koşan et al. (2007) studied this question.
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