  We study the cyclic module ${}_SR$ for a ring extension $A \| B$ with
centralizer $R$ and bimodule endomorphism ring $S = End {}_BA_B$. We show that
if $A \| B$ is an H-separable Hopf subalgebra, then $B$ is a normal Hopf
subalgebra of $A$. We observe from math.RA/0107064 and math.RA/0108067 depth
two in the role of noncommutative normality (as in field theory) in a depth two
separable Frobenius characterization of irreducible semisimple-Hopf-Galois
extensions. We prove that a depth two extension has a Galois $A$-coring
structure on $A \o_R T$ where $T$ is the right $R$-bialgebroid dual to $S$.

Rings and Algebras;Quantum Algebra