On amenability of semigroups with cancellation (Q1406387)

The authors discuss the amenability property (i.e. the fact of existence of a finitely additive invariant measure) for semigroups embedded into a group. It is proved that (a) the subsemigroup \(S\) of an amenable group is (left) right amenable iff for \(S\) the corresponding Ore condition is satisfied; (b) the amenability of a semigroup with cancellation is equivalent to the amenability of the corresponding group of quotients.