2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131792We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures between a finite set algebra and the grouplike coalgebra on two elements. The resulting 2-nilpotent algebras have particular features with respect to Hochschild (co)homology and cyclic homology.To appear in Journal of Algebra and Its ApplicationsRings and AlgebrasK-Theory and HomologyQuantum Algebra16S35, 16S38, 16E40text