2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123144Two constructions are given that describe respectively all shortest primary decompositions and all shortest uniform decompositions for left Noetherian rings. They show that these decompositions are, in general, highly non-unique.17 pagesRings and AlgebrasAlgebraic Geometry16P40, 16P70text