Geodesic
Invariant measures on semigroups and imbedding topological semigroups in topological groups
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 277-284

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In this paper the case of topological semigroups that are cancellative and right reversible is considered. It is shown (Theorem 1) that the existence in such a semigroup of a left invariant measure satisfying certain conditions is equivalent to the imbeddability of some open ideal of the given semigroup as an open subsemigroup in a locally compact group of left fractions. Conditions for imbedding topological semigroups in locally compact groups are considered in measure-theoretic terms. Bibliography: 8 titles. 
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     author = {V. V. Mukhin},
     title = {Invariant measures on semigroups and imbedding topological semigroups in topological groups},
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     url = {http://geodesic.mathdoc.fr/item/SM_1981_40_2_a10/}
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V. V. Mukhin. Invariant measures on semigroups and imbedding topological semigroups in topological groups. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 277-284. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a10/