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