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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 "summandabsorbing", if $ \forall \, x, y \in V: \ x + y \in W \; \Rightarrow \; x \inW, \; y \in W. $ These relate to tropical algebra and modules over idempotentsemirings, as well as modules over semirings of sums of squares. In previouswork, we have explored the lattice of summand absorbing submodules of a givenLZS module, especially those that are finitely generated, in terms of thelattice-theoretic Krull dimension. In this note we describe their explicitgeneration.

Generation of summand absorbing submodules