Geodesic
Note on bi-ideals in ordered semigroups and in ordered groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 6, Tome 265 (1999), pp. 198-201 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that an ordered semigroup is right and left simple if and only if it does not contain proper bi-ideals. An example is constructed showing that an ordered semigroups without proper bi-ideals need not be an ordered group. 
@article{ZNSL_1999_265_a13,
     author = {N. Kehayopulu and I. S. Ponizovskii and M. Tsingelis},
     title = {Note on bi-ideals in ordered semigroups and in ordered groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {198--201},
     year = {1999},
     volume = {265},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_265_a13/}
}
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N. Kehayopulu; I. S. Ponizovskii; M. Tsingelis. Note on bi-ideals in ordered semigroups and in ordered groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 6, Tome 265 (1999), pp. 198-201. http://geodesic.mathdoc.fr/item/ZNSL_1999_265_a13/