  The link relation on simple subcoalgebras is used for decompositions of
coalgebras. In this paper, we provide more sufficient conditions for this link
relation, and prove a formula on the products between link-indecomposable
components of Hopf algebras with the dual Chevalley property. Furthermore, we
show that each of its component is generated by a simple subcoalgebra, as a
faithfully flat module (in fact, a projective generator) over a Hopf subalgebra
which is the component containing the unit element. Our conclusions generalize
some relevant results on pointed Hopf algebras, which were established by
Montgomery in 1995.

Rings and Algebras;Quantum Algebra