  We 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)].
