2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78762We construct Artin algebras with vanishing first Hochschild Cohomology but a loop in their ordinary quiver. Some authors guessed earlier that such examples could not exist.12 pagesRings and AlgebrasRepresentation Theory16E40; 16G60Artin Algebras with Loops but no Outer Derivationstext