2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73589Let $S=\Bbbk[x_1,..., x_n]$ be a polynomial ring over a field $\Bbbk$ and $I$ a monomial ideal of $S$. It is well known that the Poincaré series of $\Bbbk$ over $S/I$ is rational. We describe the coefficients of the denominator of the series and study the multigraded homotopy Lie algebra of $S/I$.Communications in Algebra, acceptedCommutative Algebra13D07, 13D02, 13D40text