| Title:
|
A note on orthodox additive inverse semirings (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:
|
149-154 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show in an additive inverse regular semiring $(S, +, \cdot )$ with $E^{\bullet }(S)$ as the set of all multiplicative idempotents and $E^+(S)$ as the set of all additive idempotents, the following conditions are equivalent: (i) For all $e, f \in E^{\bullet }(S)$, $ef \in E^+(S)$ implies $fe\in E^+(S)$. (ii) $(S, \cdot )$ is orthodox. (iii) $(S, \cdot )$ is a semilattice of groups. This result generalizes the corresponding result of regular ring. (English) |
| Keyword:
|
additive inverse semirings |
| Keyword:
|
regular semirings |
| Keyword:
|
orthodox semirings |
| MSC:
|
16A78 |
| MSC:
|
16E50 |
| MSC:
|
16Y60 |
| MSC:
|
20M07 |
| MSC:
|
20M10 |
| idZBL:
|
Zbl 1067.16070 |
| idMR:
|
MR2124613 |
| . |
| Date available:
|
2009-08-21T12:55:15Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132936 |
| . |
| Reference:
|
[1] Chaptal N.: Anneaux dont le demi groupe multiplicatif est inverse.C. R. Acad. Sci. Paris, Ser. A-B, 262 (1966), 247–277. Zbl 0133.29001, MR 0190177 |
| Reference:
|
[2] Golan J. S.: The Theory of Semirings with Applications in Mathematics, Theoretical Computer Science. : Pitman Monographs and Surveys in Pure and Applied Mathematics 54, Longman Scientific., 1992. MR 1163371 |
| Reference:
|
[3] Howie J. M., Introduction to the theory of semigroups. : Academic Press., 1976. |
| Reference:
|
[4] Karvellas P. H.: Inverse semirings.J. Austral. Math. Soc. 18 (1974), 277–288. MR 0366991 |
| Reference:
|
[5] Zeleznekow J.: Regular semirings.Semigroup Forum 23 (1981), 119–136. MR 0641993 |
| . |
