2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110361We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.12 pages. version 2: includes omitted author contact informationCommutative Algebra13C14, 13D02text