description/proof of that 'rings - homomorphisms' isomorphism between fields is 'fields - homomorphisms' isomorphism
Topics
About: field
The table of contents of this article
Starting Context
- The reader knows a definition of field.
- The reader knows a definition of %structure kind name% homomorphism.
- The reader knows a definition of %category name% isomorphism.
Target Context
- The reader will have a description and a proof of the proposition that any 'rings - homomorphisms' isomorphism between any fields is a 'fields - homomorphisms' isomorphism.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
//
Statements:
//
2: Proof
Whole Strategy: Step 1: see that all what needs to be checked is that for each
Step 1:
As any field is a ring, calling
While only the differences of 'field' from 'ring' are being multiplicative commutative and each element's having the inverse, the commutativity is just about inside
If
So, let us check that
Step 2: