Generation of summand absorbing submodules

An R-module V over a semiring R lacks zero sums (LZS) if x + y = 0 implies x = y = 0. More generally, a submodule W of V is “summand absorbing” (SA), if, for all x,y ∈ V, x + y ∈ W ⇒ x ∈ W,y ∈ W. T...