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Title: Notes on commutative parasemifields (English)
Author: Kala, Vítězslav
Author: Kepka, Tomáš
Author: Korbelář, Miroslav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 50
Issue: 4
Year: 2009
Pages: 521-533
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: semiring
Keyword: ideal-simple
Keyword: parasemifield
Keyword: finitely generated
MSC: 16Y60
idZBL: Zbl 1203.16038
idMR: MR2583130
Date available: 2009-12-22T09:56:20Z
Last updated: 2013-09-22
Stable URL:
Reference: [1] El Bashir R., Hurt J., Jančařík A., Kepka T.: Simple commutative semirings.J. Algebra 236 (2001), 277--306. Zbl 0976.16034, MR 1808355, 10.1006/jabr.2000.8483
Reference: [2] Kala V., Kepka T.: A note on finitely generated ideal-simple commutative semirings.Comment. Math. Univ. Carolin. 49 (2008), 1--9. Zbl 1192.16045, MR 2432815
Reference: [3] Weinert H.J., Wiegandt R.: On the structure of semifields and lattice-ordered groups.Period. Math. Hungar. 32 (1996), 147--162. Zbl 0896.12001, MR 1407915, 10.1007/BF01879738


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