2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67021Given a local Cohen-Macaulay ring $(R, {\mathfrak m})$, we study the interplay between the integral closedness -- or even the normality -- of an ${\mathfrak m}$-primary $R$-ideal $I$ and conditions on the Hilbert coefficients of $I$. We relate these properties to the depth of the associated graded ring of $I$.17 pages. J. Pure and Applied Algebra, to appearCommutative Algebra13A30, 13B21, 13D40text