2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113886We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be defined as a derived functor on the category of representations of a crossed product algebra. We investigate the relationship of our theory with Hopf cyclic cohomology and also prove Morita invariance of the Hopf--Hochschild (co)homology.19 Pages. Theorem 3.7 and Corollary 4.4 modifiedK-Theory and HomologyRings and Algebrastext