2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66736Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A \ltimes M is a Gorenstein Differential Graded Algebra. As a corollary follows that A has a dualizing complex if and only if it is a quotient of a Gorenstein local Differential Graded Algebra.9 pages. To appear in Fundamenta MathematicaeCommutative AlgebraRings and AlgebrasRepresentation Theory13D25; 16E45text