In this note, some new notions of Banach homology, like I-biflatness and I-biprojectivity, for a Banach algebra A are defined, where I is a closed ideal of A. As an application, we show that M(G) is L1(G)-biprojective (I-biflat) if and only if G is a compact group (an amenable group), respectively. Also for a non-zero ideal I, we prove that if the Fourier algebra A(G) is I-biprojective, then G is a discrete group. To show the differences with classical notions we stablish some examples.
