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Keywords:
semicommutative semigroups; maher semigroups; ordered semigroups
semicommutative semigroups; maher semigroups; ordered semigroups
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.
References:
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[5] N. Kehayopulu and M. Tsingelis: On subdirecly irreducible ordered. Semigroup Forum 50 (1995), 161–177. DOI 10.1007/BF02573514 | MR 1315509
[6] N. Kehayopulu and M. Tsingelis: The embedding of and ordered semigroup in a simple one with identity. Semigroup Forum 53 (1996). MR 1406780
[7] N. Kehayopulu and M. Tsingelis: The embedding of Some ordered Semigroup. Semigroup Forum 60 (2000), 344–350. DOI 10.1007/s002339910028 | MR 1828820
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