Invariant measures on topological semigroups which have an ideal with open translation mappings (Q5931522)

A necessary and sufficient condition is given for the existence of an invariant measure on topological semigroups having an ideal with open translation mappings with respect to the elements of a semigroup. Also it is proved that in a topological semigroup \(X\) algebraically imbedded in a group there exists a nonzero left invariant measure on \(X\) iff \(X\) has an open ideal which can be topologically embedded as an open subsemigroup of a locally compact topological group.