2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114056This paper partly settles a conjecture of Costa on (n,d)-rings, i.e., rings in which n-presented modules have projective dimension at most d. For this purpose, a theorem studies the transfer of the (n,d)-property to trivial extensions of local rings by their residue fields. It concludes with a brief discussion -backed by original examples- of the scopes and limits of our results.11 pagesCommutative AlgebraRings and Algebras13D05; 13B02text