Hi guys,

I'm scheduled to see my lecturer about this problem, but he isn't available until next week, and I feel that I am likely to get a clearer explanation here.

This is for a Galois Theory course, and he states the following theorem,

Let

be a subring of

and fix

. Then the smallest subring of

that contains both

and

is equal to

and then he writes this subring as

.

Then, he writes an example,

, and concludes that

This is fine. The problem is when he introduces subrings of two elements. He claims