Subject: Algebraic question
Date: Sat, 16 Aug 2003 13:32:08 -0400
From: Justin Smith <jsmith@drexel.edu>

Here's a questions for the topology mailing list:

Suppose we have an infinite sequence

... V_k \subseteq V_{k-1} \subseteq ... V_1

of Z-modules such that each V_i is a direct summand of V_{i-1}
(and therefore, of V_1).

What can one say about V_{\infty} = intersection of all the V_i?

Is it a direct summand of V_1?

We cannot assume that the modules are finitely generated or free
(although they may be Z-free).
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