Torsion–almost-divisibility conjecture for finitely generated commutative semirings

Let $S$ be a finitely generated commutative semiring. The additive semigroup $S(+)$ is the semigroup consisting of the elements of $S$ under addition.

Torsion–almost-divisibility conjecture. The semigroup $S(+)$ is torsion if and only if $S(+)$ is almost-divisible.

This conjecture asks whether almost-divisibility characterizes torsion in the additive semigroups of finitely generated commutative semirings. It is presented as a weaker analogue of divisibility, which is equivalent to idempotency for additive semigroups of finitely generated commutative parasemifields; its resolution is not indicated here.