TITLE: Is there a Galois correspondence for ring extensions?
QUESTION [24 upvotes]: Given an ring extension of a (commutative with unit) ring, Is it possible to give a "good" notion of "degree of the extension"?. By "good", I am thinking in a degree which allow us, for instance, to define finite ring extensions and generalize in some way the Galois' correspondence between field extensions and subgroups of Galois' group.
I suppose one can call a ring extension $A\subset B\ $ finite if $B$ is finitely generated as an $A$-module, and the degree would be the minimal number of generators, but is that notion enough to state a correspondence theorem?
Thanks in advance!

REPLY [4 votes]: see related question
and SGA1 as well as Lenstra's notes 
and Manjul Bhargava and Matt Satriano's paper