MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

2 edited title

1

# Is there a Galois' correspondence for ring extensions?

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?