| Title:
|
Semirings embedded in a completely regular semiring (English) |
| Author:
|
Sen, M. K. |
| Author:
|
Maity, S. K. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
143-148 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Recently, we have shown that a semiring $S$ is completely regular if and only if $ S$ is a union of skew-rings. In this paper we show that a semiring $S$ satisfying $a^2=na$ can be embedded in a completely regular semiring if and only if $S$ is additive separative. (English) |
| Keyword:
|
completely regular semiring |
| Keyword:
|
skew-ring |
| Keyword:
|
b-lattice |
| Keyword:
|
archimedean semiring |
| Keyword:
|
additive separative semiring |
| MSC:
|
16A78 |
| MSC:
|
16E50 |
| MSC:
|
16Y60 |
| MSC:
|
20M07 |
| MSC:
|
20M10 |
| idZBL:
|
Zbl 1067.16069 |
| idMR:
|
MR2124612 |
| . |
| Date available:
|
2009-08-21T12:55:08Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132946 |
| . |
| Reference:
|
[1] Clifford A. H., Preston G. B.: The algebraic theory of semigroups. : Amer. Math. Soc., Providence Rhode Island, Vol. I., 1961. MR 0132791 |
| Reference:
|
[2] Grillet M. P.: Semirings with a completely simple additive semigroup.J. Austral. Math. Soc. A 20 (1975), 257–267. Zbl 0316.16039, MR 0491843 |
| Reference:
|
[3] Hebisch, U, Weinert H. J.: Semirings, Algebra Theory, Applications in Computer Science, Series in Algebra. : Vol. 5, World Scientific, Singapore., 1998. MR 1704233 |
| Reference:
|
[4] Sen M. K., Maity S. K., Shum K. P.: On completely regular semirings.(submitted). Zbl 1115.16026 |
| . |
