2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62062We study a certain class of non-maximal rank contractions of the nilpotent Lie algebra $\frak{g}_{m}$ and show that these contractions are completable Lie algebras. As a consequence a family of solvable complete Lie algebras of non-maximal rank is given in arbitrary dimension.Latex, 9 pagesRings and Algebras17B10, 17B30text