Geodesic
On the embedding of ordered semigroups into ordered group
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 303-313
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 06F05, 20M99
Keywords: semicommutative semigroups; maher semigroups; ordered semigroups 
@article{CMJ_2004_54_2_a3,
     author = {Ibrahim, Mohammed Ali Faya},
     title = {On the embedding of ordered semigroups into ordered group},
     journal = {Czechoslovak Mathematical Journal},
     pages = {303--313},
     year = {2004},
     volume = {54},
     number = {2},
     mrnumber = {2059252},
     zbl = {1080.06020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a3/}
}
TY  - JOUR
AU  - Ibrahim, Mohammed Ali Faya
TI  - On the embedding of ordered semigroups into ordered group
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 303
EP  - 313
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a3/
LA  - en
ID  - CMJ_2004_54_2_a3
ER  - 
%0 Journal Article
%A Ibrahim, Mohammed Ali Faya
%T On the embedding of ordered semigroups into ordered group
%J Czechoslovak Mathematical Journal
%D 2004
%P 303-313
%V 54
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a3/
%G en
%F CMJ_2004_54_2_a3
Ibrahim, Mohammed Ali Faya. On the embedding of ordered semigroups into ordered group. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 303-313. http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a3/

[1] M. Faya Ibrahim: Semigroup Presentations. Ph.D. Thesis, University of St. Andrews, 1997.

[2] L. Fuchs: Partially Ordered Algebraic System. Pergamon Press, Oxford, 1963. | MR

[3] P. Higgins: Techniques of Semigroup Theory. Clarendon Press, Oxford University Press, New York, 1992. | MR | Zbl

[4] J. Howie: Fundamentals of Semigroup Theory. Oxford University Press, New York, 1992. | MR

[5] N. Kehayopulu and M. Tsingelis: On subdirecly irreducible ordered. Semigroup Forum 50 (1995), 161–177. | DOI | MR

[6] N. Kehayopulu and M. Tsingelis: The embedding of and ordered semigroup in a simple one with identity. Semigroup Forum 53 (1996). | MR

[7] N. Kehayopulu and M. Tsingelis: The embedding of Some ordered Semigroup. Semigroup Forum 60 (2000), 344–350. | DOI | MR