2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172214In this paper, we make the notion of approximating an Artinian local ring by a Gorenstein Artin local ring precise using the concept of Gorenstein colength. We also answer the question as to when the Gorenstein colength is at most two.The title and layout have changed, has been shortened to 9 pages. Published in Journal of AlgebraCommutative Algebratext