Depth Two and the Galois Coring
Abstract
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 Hseparable 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 semisimpleHopfGalois extensions. We prove that a depth two extension has a Galois $A$coring structure on $A ø_R T$ where $T$ is the right $R$bialgebroid dual to $S$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2004
 arXiv:
 arXiv:math/0408155
 Bibcode:
 2004math......8155K
 Keywords:

 Rings and Algebras;
 Quantum Algebra;
 16A24
 EPrint:
 9 pages