Finite-dimensional right ideals in some algebras associated with a locally compact group

Let be a discrete group, a commutative discrete cancellative semigroup or a locally compact abelian group. Let be the space of bounded, uniformly continuous, complex-valued functions on With an Arens-type product, the conjugate becomes a Banach algebra. We prove, that unlike left ideals, finite-dimensional right ideals exist in if and only if is compact.