2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126462Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the following result. Let $R$ be a commutative Noetherian ring and $a$ an ideal in the Jacobson radical of $R$. Let $\hat{R}^a$ be the $a$-adic completion of $R$. If $M$ is a finitely generated $R$-module such that $\ext^i_R(\hat{R}^a,M)=0$ for all $i\neq 0$, then $M$ is $a$-adically complete.10 pages; proof of Theorem A revised; Theorem B added; to appear in Proceedings of the American Mathematical SocietyCommutative AlgebraRings and Algebras13B35, 13D07, 13D25, 13D45, 13J10text