Notes on commutative parasemifields. (English) Zbl 1203.16038

Kala, Vítězslav; Kepka, Tomáš; Korbelář, Miroslav

Commentat. Math. Univ. Carol. 50, No. 4, 521-533 (2009).

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).

Reviewer: Petr Němec (Praha)

MSC:

16Y60	Semirings
12K10	Semifields

Keywords:

commutative semirings; ideal-simple semirings; finitely generated parasemifields