2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61246We prove the existence of two long exact sequences relating the Hochschild cohomology of a triangular matrix algebra with the Hochschild homology of its component subalgebras. We also study the structure of the maps of the first sequence.8 pages. Major conceptual changesK-Theory and HomologyRings and Algebras14E40; 16S50text