Invariant measures on semigroups and imbedding topological semigroups in topological groups

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.
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