Some results on (IEZ)-modules

Abstract

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.