Biflatness of certain semigroup algebras

In the present paper‎, ‎we consider biflatness of certain classes of semigroup algebras‎. ‎Indeed‎, ‎we give a necessary condition for a band semigroup algebra‎ ‎to be biflat and show that this condition is not sufficient‎. ‎Also‎, ‎for a certain class of inverse semigroups $S,$ we show that the‎ ‎biflatness of $\ell^{1}(S)^{\prime\prime}$ is equivalent to the‎ ‎biprojectivity of $\ell^{1}(S)$‎.