2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115577Given a Noetherian local ring (R,m) it is shown that there exists an integer l such that R is Gorenstein if and only if some system of parameters contained in m^l generates an irreducible ideal. We obtain as a corollary that R is Gorenstein if and only if every power of the maximal ideal contains an irreducible parameter ideal.9 pages; submitted; Replacement: Coauthor H. Sakurai added, reference to work of J. R. Strooker added, introduction shortenedCommutative Algebra13D45 (Primary) 13H10 (Secondary)text