Let $Ok$ be a area containing an integral area $D$ and $F$ be the
area of quotients of $D$. Then $Ok$ comprises a area isomorphic to
I’ve appeared over some options however I don’t perceive the final strategy. That’s, they begin by defining a map $phi:F to Ok$, and present $phi$ is an isomorphism. I perceive what follows after that, however I’m having bother with the beginning of this strategy.
Now, the principle level of this drawback is to point out that $F$ is the smallest area containing D. And proving these sorts of issues entails assuming any area containing $F$ shall be isomorphic to $F$ that means that we are able to’t scale back $F$ any additional.
Holding this in thoughts, I’m battling the next questions:
- Why does the strategy highlighted above make sense?
- Why even phrase the query like this if we aren’t going to point out an imaginary sub-field of $Ok$ and present it to be isomorphic to $F$?
- Is it doable to assemble a proof with the next define:
Let $F’$ be a area s.t. $F’ subset Ok$, then present $F cong F’$.