2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70301We prove that the arithmetic degree of a graded or local ring is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideals $I$ in $A$. In particular, if $Spec (A)$ is equidimensional and has an embedded component in dimension $i$, then the normal cone of $Spec (A)$ along $V(I)$ has an embedded component in dimension $i$ too.13 pagesCommutative AlgebraAlgebraic Geometry13H15; 13A30text