| Title:
|
Bi-ideal-simple semirings (English) |
| Author:
|
Flaška, Václav |
| Author:
|
Kepka, Tomáš |
| Author:
|
Šaroch, Jan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
391-397 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Commutative congruence-simple semirings were studied in [2] and [7] (but see also [1], [3]--[6]). The non-commutative case almost (see [8]) escaped notice so far. Whatever, every congruence-simple semiring is bi-ideal-simple and the aim of this very short note is to collect several pieces of information on these semirings. (English) |
| Keyword:
|
bi-ideal-simple |
| Keyword:
|
semiring |
| Keyword:
|
zeropotent |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 1106.16048 |
| idMR:
|
MR2174518 |
| . |
| Date available:
|
2009-05-05T16:51:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119534 |
| . |
| Reference:
|
[1] Eilhauer R.: Zur Theorie der Halbkörper, I.Acta Math. Acad. Sci. Hungar. 19 (1968), 23-45. Zbl 0183.04202, MR 0222120 |
| Reference:
|
[2] El Bashir R., Hurt J., Jančařík A., Kepka T.: Simple commutative semirings.J. Algebra 236 (2001), 277-306. Zbl 0976.16034, MR 1808355 |
| Reference:
|
[3] Golan J.: The Theory of Semirings with Application in Math. and Theoretical Computer Science.Pitman Monographs and Surveys in Pure and Applied Mathematics 54 Longman, Harlow (1992). MR 1163371 |
| Reference:
|
[4] Hebisch U., Weinert H.J.: Halbringe. Algebraische Theorie und Anwendungen in der Informatik.Teubner Stuttgart (1993). Zbl 0829.16035, MR 1311247 |
| Reference:
|
[5] Hutehins H.C., Weinert H.J.: Homomorphisms and kernels of semifields.Period. Math. Hungar. 21 (1990), 113-152. MR 1070951 |
| Reference:
|
[6] Koch H.: Über Halbkörper, die in algebraischen Zahlkörpern enhalten sind.Acta Math. Acad. Sci. Hungar. 15 (1964), 439-444. MR 0168609 |
| Reference:
|
[7] Mitchell S.S., Fenoglio P.B.: Congruence-free commutative semirings.Semigroup Forum 37 (1988), 79-91. Zbl 0636.16020, MR 0929445 |
| Reference:
|
[8] Monico C.: On finite congruence-simple semirings.J. Algebra 271 (2004), 846-854. Zbl 1041.16041, MR 2025553 |
| . |
