  An $R$-module $V$ over a semiring $R$ lacks zero sums (LZS) if $ x +y = 0 \;
\Rightarrow \; x = y = 0$. More generally, asubmodule $W$ of $V$ is "summand
absorbing", if $ \forall \, x, y \in V: \ x + y \in W \; \Rightarrow \; x \in
W, \; y \in W. $ These relate to tropical algebra and modules over idempotent
semirings, as well as modules over semirings of sums of squares. In previous
work, we have explored the lattice of summand absorbing submodules of a given
LZS module, especially those that are finitely generated, in terms of the
lattice-theoretic Krull dimension. In this note we describe their explicit
generation.
