| Title:
|
On the embedding of ordered semigroups into ordered group (English) |
| Author:
|
Ibrahim, Mohammed Ali Faya |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
303-313 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of $L$-maher and $R$-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered $L$ or $R$-maher semigroup can be embedded into an ordered group. (English) |
| Keyword:
|
semicommutative semigroups |
| Keyword:
|
maher semigroups |
| Keyword:
|
ordered semigroups |
| MSC:
|
06F05 |
| MSC:
|
20M99 |
| idZBL:
|
Zbl 1080.06020 |
| idMR:
|
MR2059252 |
| . |
| Date available:
|
2009-09-24T11:12:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127889 |
| . |
| Reference:
|
[1] M. Faya Ibrahim: Semigroup Presentations.Ph.D. Thesis, University of St. Andrews, 1997. |
| Reference:
|
[2] L. Fuchs: Partially Ordered Algebraic System.Pergamon Press, Oxford, 1963. MR 0171864 |
| Reference:
|
[3] P. Higgins: Techniques of Semigroup Theory.Clarendon Press, Oxford University Press, New York, 1992. Zbl 0744.20046, MR 1167445 |
| Reference:
|
[4] J. Howie: Fundamentals of Semigroup Theory.Oxford University Press, New York, 1992. MR 1455373 |
| Reference:
|
[5] N. Kehayopulu and M. Tsingelis: On subdirecly irreducible ordered.Semigroup Forum 50 (1995), 161–177. MR 1315509, 10.1007/BF02573514 |
| Reference:
|
[6] N. Kehayopulu and M. Tsingelis: The embedding of and ordered semigroup in a simple one with identity.Semigroup Forum 53 (1996). MR 1406780 |
| Reference:
|
[7] N. Kehayopulu and M. Tsingelis: The embedding of Some ordered Semigroup.Semigroup Forum 60 (2000), 344–350. MR 1828820, 10.1007/s002339910028 |
| . |
