2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71906Let $(R,\m)$ be a Noetherian local ring. Consider the notion of homological dimension of a module, denoted H-dim, for H= Reg, CI, CI$_*$, G, G$^*$ or CM. We prove that, if for a finite $R$-module $M$ of positive depth, $\Hd_R({\m}^iM)$ is finite for some $i \geq \reg(M)$, then the ring $R$ has property H.7 pages. To appear in Contemporary MathCommutative Algebra13H05; 13D10text