The Construction Of a Simplicial Resolution Of l² Where l Is Square-Free Monomial Ideal.

Abstract

Let R=ĸ[x_1‚…‚x_n] be the polynomial ring in n variables, and I=(m_1‚…‚m_q) a square-free monomial ideal in R. We consider the ideal I²=({m_i m_j:i‚j}) to be the monomial ideal generated by at most ((q+1)¦2) generators. We study the construction of a simplicial complex labeled by the monomials of l² which supports a free resolution of l².