2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103871The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The generalization of Maschke's theorem and homological integrals are the keys to study noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.30 pagesQuantum AlgebraRings and Algebras16A62,16W30text