| 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:
|
http://hdl.handle.net/10338.dmlcz/137443 |
| . |
| 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 |
| . |
