2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128593We study the Hochschild and cyclic homologies of noncommutative monogenic extensions. As an aplication we compute the Hochschild and cyclic homologies of the rank~1 Hopf algebras introduced by L. Krop and D. Radford in [Finite dimensional Hopf algebras of rank 1 in characteristic 0, Journal of Algebra 302, no. 1, 214-230} (2006)].22 pagesK-Theory and Homology16E40; 16S36text