| Title:
|
Green's $\mathcal{D}$-relation for the multiplicative reduct of an idempotent semiring (English) |
| Author:
|
Pastijn, F. |
| Author:
|
Zhao, Xianzhong |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
77-93 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The idempotent semirings for which Green’s ${\cal D}$-relation on the multiplicative reduct is a congruence relation form a subvariety of the variety of all idempotent semirings. This variety contains the variety consisting of all the idempotent semirings which do not contain a two-element monobisemilattice as a subsemiring. Various characterizations will be given for the idempotent semirings for which the ${\cal D}$-relation on the multiplicative reduct is the least lattice congruence. (English) |
| Keyword:
|
idempotent semiring |
| Keyword:
|
variety |
| Keyword:
|
Green relations |
| Keyword:
|
band |
| Keyword:
|
bisemilattice |
| MSC:
|
16Y60 |
| MSC:
|
20M10 |
| idZBL:
|
Zbl 1051.16027 |
| idMR:
|
MR1761613 |
| . |
| Date available:
|
2008-06-06T22:25:21Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107721 |
| . |
| Reference:
|
[1] Howie J. M.: Fundamentals of Semigroup Theory.Oxford Science Publications, Oxford, 1995. Zbl 0835.20077, MR 1455373 |
| Reference:
|
[2] McKenzie R., and A. Romanowska: Varieties of $\cdot $-distributive bisemilattices.Contributions to General Algebra, (Proc. Klagenfurt Conf., Klagenfurt 1978), 213–218, Heyn, Klagenfurt, 1979. MR 0537422 |
| Reference:
|
[3] Pastijn F., and Y. Q. Guo: The lattice of idempotent distributive semiring varieties.Science in China (Series A) 42 (8) (1999), 785–804. MR 1738550 |
| Reference:
|
[4] Sen M. K., Guo Y. Q., and K. P. Shum: A class of idempotent semirings.preprint. MR 1828821 |
| . |
