- #1

AcidRainLiTE

- 90

- 2

## 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.