Structural decomposition of monomial resolutions

We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decomposition has multiple applications. In some concrete cases, we use it to construct minimal resolutions of classes of monomial ideals; in other cases, we use it to compute projective dimensions. To illustrate the effectiveness of the structural decomposition, we give a new proof of a classic theorem by Charalambous that states the following: let k be a field, and M an Artinian monomial ideal in S=k[x1,…,xn]; then, for all i, bi(S/M)≥(ni).