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Abstract:
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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 (C2).
(ii) If X M,X = Mi (with i 2 {1, ..., n}), then X M.
(2) 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 nonsingular (IEZ)−module. Then,
M is a continuous module. |