2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70339Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the condition for $A[I t]$ to be generalized Cohen-Macaulay.Commutative Algebra13A30, 13D45text