Cyclic homology of monogenic extensions in the noncommutative setting

We study the Hochschild and cyclic homology of noncommutative monogenic extensions. As an application we compute the Hochschild and cyclic homology of the rank 1 Hopf algebras introduced in [L. Krop, D. Radford, Finite dimensional Hopf algebras of rank 1 in characteristic 0, Journal of Algebra 302 (1) (2006) 214–230].