  Commutative semirings with divisible additive semigroup are studied. We show
that an additively divisible commutative semiring is idempotent, provided that
it is finitely generated and torsion. In case that a one-generated additively
divisible semiring posseses no unit, it must contain an ideal of idempotent
elements. We also present a series of open questions about finitely generated
commutative semirings and their equivalent versions.
