Biflatness of semigroup algebras

We shall study the biflatness of the convolution algebra ℓ ¹(S) for a semigroup S. We show that for any semigroup S such that ℓ ¹(S) is biflat the canonical partial ordering on the idempotents must be uniformly locally finite. We use this to characterize the biflatness of ℓ ¹(S) for an inverse semigroup S.