Galois Objects of Finitely Generated Projective Hopf Algebras

摘要

Let C be the category of cocommutative coalgebras over a commutative ring R and let H be a group object in C, i.e., let H be a cocommutative Hopf algebra. Assume that H is a finitely generated, projective R-module and that the integrals (of 4) in H* #x2261; HomR(H, R) are cocommutative elements. We will show that any Galois H-object (as defined in 3, Def. 1.2, p. 8) is a finitely generated, projective R-module.