  In this note, we are working within the category $\rmod$ of (unitary, left)
$R$-modules, where $R$ is a {\bf countable} ring. It is well known (see e.g.
Kie{\l}pi\'nski & Simson [5], Theorem 2.2) that the latter condition implies
that the (left) pure global dimension of $R$ is at most 1. Given an infinite
index set $A$, and a family $M_\al\in\rmod$, $\al\in A$ we are concerned with
the conditions as to when the $R$-module $$\prod/\coprod=\prod_{\al\in
A}M_\al/\bigoplus_{\al\in A}M_\al$$ is or is not algebraically compact. There
are a number of special results regarding this question and this note is meant
to be an addition to and a generalization of the set of these results. Whether
the module in the title is algebraically compact or not depends on the numbers
of algebraically compact and non-compact modules among the components $M_\al$.
