The conjecture on additive idempotence of finitely generated semifields

A semifield is a commutative semiring whose multiplicative structure is a group. A semiring is finitely generated as a semiring when it is generated by finitely many elements under addition and multiplication. It is additively idempotent when $a+a=a$ for every element $a$. Additive-idempotence conjecture. Every semifield which is finitely generated as a semiring is additively idempotent. This conjecture is posed in the context of classifying ideal-simple commutative semirings and is described as extending the classical result for fields finitely generated as rings; its resolution is not supplied here.