2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65128The aim of this paper is to obtain a uniform bound for a certain class of submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let $M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal of $R$ generated by a system of parameters on $M$. Let $N$ be a submodule of $M$ with $\depth M/N\ge d-1$. Then $\ell(N/\frak qN)\le\ell(M/\frak qM)$.5 pagesCommutative Algebra13C99; 13E15; 13H10text