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Notes on commutative parasemifields. (English) Zbl 1203.16038

In the paper a thorough investigation of parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) is continued. Main emphasis is laid on the problem when a parasemifield is finitely generated. In particular, it is shown that if a parasemifield \(S\) contains the set of positive rationals \(\mathbb{Q}^+\) as a subparasemifield, \(a\in S\) and \(S\) is generated by \(\mathbb{Q}^+\cup\{a\}\) then \(S\) is not finitely generated as a semiring (Theorem 4.21).

MSC:

16Y60 Semirings
12K10 Semifields
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