Two constructions with galois objects

Abstract

Let G, H be Hopf algebras which are finitely generated projective modules over the ground ring R. We use the ideal of integrals of the dual Hopf algebra H^* of H to give a new description of Gal(l)(A) where A ∈ Gal(H) and i: G → H is a Hopf algebra morphism which is both monk and epic in the category of finitely generated projective R-modules. We also give a new description of the group operation on Gal(H) for H cocommutative