semicommutative semigroups; maher semigroups; ordered semigroups
It was shown in  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  to show that any left reversible cancellative ordered $L$ or $R$-maher semigroup can be embedded into an ordered group.
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