2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210583We consider the first Weyl algebra, A, in the Euler gradation, and completely classify graded rings B that are graded equivalent to A: that is, the categories gr-A and gr-B are equivalent. This includes some surprising examples: in particular, we show that A is graded equivalent to an idealizer in a localization of A. We obtain this classification as an application of a general Morita-type characterization of equivalences of graded module categories.38 pages; minor changes to final published versionRings and Algebras16W50; 16D90text