What does it mean for a Ring to be Stabilized by a map

[AcidRainLiTE]

Homework Statement

Let D be a division ring, C its center and let S be a division subring of D which is stabilized by every map x -> dxd^-1, d≠0 in D. Show that either S = D or S is a subset of C.


2. The attempt at a solution
I haven't actually started working on it yet because I am not sure what it asking. What does it mean for a subring to be stabilized by a map? And what is x? Is it an element of D?

I am familiar with the stabilizer of an element, but the above terminology is confusing me.

 

[quasar987]

It means that dSd^-1=S for all nonzero d. (same definition as the stabilizer of an element but with the set S substituted in its place!)

I think a more common terminology would be to say

"...and let S be a division subring of D which is stable under the action by every map x -> dxd-1, d≠0 in D"