Geodesic
On the embedding of ordered semigroups into ordered group
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 303-313

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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 
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/
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     zbl = {1080.06020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a3/}
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