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