Some module cohomological properties of Banach algebras

We find some relations between module biprojectivity and module biflatness of Banach algebras $\mathcal A$ and $\mathcal B$ and their projective tensor product $\mathcal A \mathbin{\widehatøtimes}\mathcal B$. For some semigroups $S$, we study module biprojectivity and module biflatness of semigroup algebras $l^1(S)$.