A note on finitely generated ideal-simple commutative semirings

Vítězslav Kala; Tomáš Kepka

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Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield $S$ contains $ℚ^{+}$ as a subparasemifield and is generated by $ℚ^{+} \cup {a}$ , $a \in S$ , as a semiring, then $S$ is (as a semiring) not finitely generated.