A module M is called (IEZ)−module if for the submodules A, B, C of M such that A ∩ B = A ∩ C = B ∩ C = 0, then A ∩ (B ⊕ C) = 0. It is shown that: (1) Let M1 , ., Mn be uniform local modules such that Mi does not embed in J(Mj ) for any i, j = 1, ., n. Suppose that M = M1 ⊕ . ⊕ Mn is a (IEZ)−module. Then (a) M satisfies (C3 ). (b) The following assertions are equivalent: (i) M satisfies (C 2 )