Geodesic
Notes on commutative parasemifields
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 521-533 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\Bbb Q^+$ 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.
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.
Classification : 16Y60
Keywords: semiring; ideal-simple; parasemifield; finitely generated 
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     title = {Notes on commutative parasemifields},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     year = {2009},
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}
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Kala, Vítězslav; Kepka, Tomáš; Korbelář, Miroslav. Notes on commutative parasemifields. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 521-533. http://geodesic.mathdoc.fr/item/CMUC_2009_50_4_a2/