All Questions
4
questions
76
votes
7
answers
33k
views
Is an automorphism of the field of real numbers the identity map?
Is an automorphism of the field of real numbers $\mathbb{R}$ the identity map?
If yes, how can we prove it?
Remark An automorphism of $\mathbb{R}$ may not be continuous.
- 42.9k
10
votes
2
answers
1k
views
Are the real numbers the unique Dedekind-complete ordered set?
A totally ordered set is Dedekind-complete if any subset which has an upper bound also has a least upper bound. Now any two ordered fields which are Dedekind-complete are order-isomorphic as well as ...
- 10.3k
1
vote
3
answers
172
views
What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$
We know that $\mathbb R \times \mathbb R$ forms a field under addition and multiplication defined as $(a,b)+(c,d)=(a+c,b+d)$ ; $(a,b)*(c,d)=(ac-bd,ad+bc)$ ; is there any other way to make $\mathbb R \...
- 8,387
3
votes
1
answer
136
views
Is there an ordered field with distinct subfields isomorphic to the reals?
Is there an ordered field with distinct subfields isomorphic to the field $\mathbb R$ of real numbers?
- 19.9k